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2018_ICERM_Presentation.ipynb
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2018_ICERM_Presentation.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"from viewLatex import viewLatex"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"slideshow": {
"slide_type": "notes"
}
},
"outputs": [],
"source": [
"def contact_vector(dw):\n",
" x = 0\n",
" y = 0\n",
" vector = [dw.number_of_touch_points()]\n",
" for i,step in enumerate(dw):\n",
" if step == 1:\n",
" y += 1\n",
" d = y - x\n",
" c = 0\n",
" xx = x\n",
" yy = y\n",
" for k in range(i+1,len(dw)):\n",
" dd = yy - xx\n",
" if dd == d:\n",
" c+=1\n",
" elif dd < d:\n",
" break\n",
" xx, yy = (xx+1, yy) if dw[k] == 0 else (xx, yy+1)\n",
" c -= 1\n",
" vector.append(c)\n",
" \n",
" else:\n",
" x += 1\n",
" return vector[:-1]\n",
"\n",
"def rise_vector(dw):\n",
" vector = []\n",
" r = 0\n",
" for step in dw:\n",
" if step == 0:\n",
" vector.append(r)\n",
" r = 0\n",
" else:\n",
" r+=1\n",
" return vector"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# The Rise contact involution on Tamari Intervals\n",
"\n",
"**Viviane Pons** -- July, 24th 2018 -- ICERM"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
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mEMjls9MXLBeKacPEWrpgBoIUy2enL1kuFNOCibYUf9BOng0HafjSxJLlUjEtmH9hLSkJCSkMX5pYtFwqpq2ZPk9/1yUwpOm7PIuWi8V0PA3bKcEhhem7PMuWi8UMhRkDpPErZsuWy8UMgRkHpDB+xcxguVzMR2NGA2n+5qPB0lDMKWZSycpxZmO+NHUqIkhh/uajydJQzAlmC5ENpzzhc1Q6zLggLV/INVmaijnGTOq2lVI5dDPLZ5ixQQrLF3KNlqZijjGPqp1L6jTMTZYjzAghbd8TN1oaizl5mKft6JOdQzPLNB1ixgcpbN8TN1sai6l5Ni8c9pmFFCPM59ggreMLzJbmYs4x943DBLLTRVOVki/+gFjGF1gszcWcYmZS5vKG+ekJkFv5ylLEjWmbqmGxtBRT9zBvboMGn34A8ny9ZDsJLmZM21QNm6WlmLpXQIkiTs/t9g/xYlqHvdgsbcUcY2bdwKhUKdJeM83lKZWqZJSc1mEvVktbMceYddeqEyZpoFmWtqnUMY1wHpp9BpHV0lrMMaZSbTVTpxGQMsqHuX0Gkd3SWswx5nkJgEq5LCkgnS59nwBGY9kt7cUcYxZSpqmsHV6aJ7lSdR7ZWiGA0VgAS3sxZ8eZiSw3NjUYMrENYAkoZsjPgB4TyMQ2iCWgmFvHBA0ShFhCirlxTNAgQZAlpJibxoTNtwRZgoq5ZUzYfEuYJaiY28UEjl2FWcKKuVlM4NhVoCWsmBvFhE4DBloCi7lNTOg0YKglsJhbxAQPqYZaQou5QUzwkGqwJbSYm8OEz04HW4KLuTVM+Ox0uCW4mNvCRIz0h1vCi7kpTMRIf4QlvJgbwsSsNIGwRBRzO5iYlSYwlohibgUTtQAKxhJTzI1gohZAQVliirkJTNy6PChLVDG3gIlblwdniSrm+jGRy0XhLHHFXD0mcrkopCWumCvHxK5ihrREFnPdmNhVzLCWyGKuGRO9uB7WElvMFWOiF9dDW2KLuVpM/JqPaEt0MdeKiV/zEW+JLuY6MQlLkeIt8cVcJSZhKVKCJb6YK8SkrJBLsCQUc32YlBVyKZaEYq4Nk7RwM8WSUsyVYZIWbiZZUoq5KkzaeuIkS1Ix14RJW0+cZkkq5nowicvc0yxpxVwNJnGZe6IlrZgrwSTWkmpJLOY6MIm1JFu+/kMbzvj29YEotFBrSbbccKi1PGF+YctRyLXkzEKvJWcSrqXHfOFa+svrt9D3YNVJKympYymyJulGrqR76o1L+vDQ5HJBly3wG9lkosiJ9yVVfYhDFuXx9OO4o1xS7i43mrQTtnbVI7AsSeqinTtJxahkF+JcwOwsQBkwcnos9Hc666YYZRFM0CnqY7dRxIdpXwfqxeX58pL2p+wxper+aSj99pujou7tupzbcDySb727AuJes8c8nCe/5fVdgDDJlcjk0W1cV0beXRW1koVIiJfvMfsxejltAJzPKJUc2+dkl+vI6X+LpFYH4oN8jhl8p6lU+xAdjDl8hkycfBpeReqys2oPB3aDSv0CHHV5w0xjwuxqdZs4+fQMyGgQr8uwr2RXHE/lvFX7xXzDo7/iGXPf3/ddDJjdP40iX8PeYSPK1qHYEYeHjh/mEWD2ig6PEUn/O4jD+VYr2nPHdJ95HyFEKudmumxEf9GCdnzWYzbnaZm5y9BMP+nn5VOn9IrrjoKU+oxY0A4RrwftXa9rh2UDfKVpD/JKh/2NC6Y8HwhI0kF/1mMW3bzMso5gtu2+kWl5cHhCVi6vPGRepinpQDPPD0rleVvt/WnXmx6cXsl5SykTl9cOpdObX0Xiduv+roTD4XA4HA4ngvyNPPvt5SX0PY44X3HnBL6M39PkjILDfPnxe+g7HHNQmGxpDgaTLS1BYLKlLXBMtrQGjMmW9kAx2RIQICZbQgLDZEtQQJhsCQsEky2BAWCyJTR2TLYEx4rJlvDYMNkSEQsmW2JixmRLVIyYbImLCZMtkTFgsiU2y5hsic4iJlvis4TJloQsYLIlJXpMtiRFi8mWtOgw2ZIYDSZbUjPHZEtyZphsSc8Uky0dMsFkS5e8vQ1/Y0t/+fQvW/rLb+5XweFwOByOPWklqzimNa4/VVOIoolgusYGUqqy+xnBeI31p58ARJ3eyRmmnzyjwo8k2kAumOGHZW0ghwsm7zTdIzvFvQo/E28DOR8VyQiGsm4hxU4mcn/gfaanZE5j/TiTZIo6TZszyPkVkKx5l+khssXMan6nw0eKXZkmLvMmOYMUjvMmx/k/y+xvMNmy17AAAAAldEVYdGRhdGU6Y3JlYXRlADIwMjAtMDYtMTZUMTQ6NTg6NDUrMDI6MDAGOkHGAAAAJXRFWHRkYXRlOm1vZGlmeQAyMDIwLTA2LTE2VDE0OjU4OjQ1KzAyOjAwd2f5egAAABR0RVh0cGRmOlZlcnNpb24AUERGLTEuNSAFXAs5AAAAAElFTkSuQmCC\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tip = TamariIntervalPoset(10, [(2,5), (3,4), (4,5), (6,7), (8,10), (9,10), (3,2), (4,2), (6,5), (7,5), (8,5), (10,5), (9,8)])\n",
"viewLatex(tip)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## The Tamari lattice"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"P = Poset({dw: [bt.to_dyck_word_tamari() for bt in dw.to_binary_tree_tamari().tamari_succ()] for dw in DyckWords(3)})\n",
"viewLatex(P)"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Some statistics on Dyck Paths"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"dw = DyckWord([1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0])\n",
"viewLatex(dw)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"2\n",
"2\n"
]
}
],
"source": [
"print (dw.number_of_touch_points())\n",
"print (dw.number_of_initial_rises())"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2, 2, 0, 1, 0, 2, 0, 2, 0, 1]\n",
"[2, 2, 0, 0, 2, 2, 2, 0, 0, 0]\n"
]
}
],
"source": [
"print (contact_vector(dw))\n",
"print (rise_vector(dw))"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 10,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 3\n",
"sorted([contact_vector(dw) for dw in DyckWords(n)]) == sorted([rise_vector(dw) for dw in DyckWords(n)])"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"False"
]
},
"execution_count": 11,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 3\n",
"sorted([[contact_vector(dw), rise_vector(dw)] for dw in DyckWords(n)]) == \\\n",
"sorted([[rise_vector(dw), contact_vector(dw)] for dw in DyckWords(n)])"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"def contact_partition(dw):\n",
" v = contact_vector(dw)\n",
" v.sort()\n",
" v.reverse()\n",
" return v\n",
"\n",
"def rise_partition(dw):\n",
" v = rise_vector(dw)\n",
" v.sort()\n",
" v.reverse()\n",
" return v"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[2, 2, 0, 1, 0, 2, 0, 2, 0, 1]\n",
"[2, 2, 2, 2, 1, 1, 0, 0, 0, 0]\n"
]
}
],
"source": [
"dw = DyckWord([1,1,0,1,1,0,0,0,1,1,0,1,1,0,1,1,0,0,0,0])\n",
"print (contact_vector(dw))\n",
"print (contact_partition(dw))"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 16,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 3\n",
"sorted([[contact_partition(dw), rise_partition(dw)] for dw in DyckWords(n)]) == \\\n",
"sorted([[rise_partition(dw), contact_partition(dw)] for dw in DyckWords(n)])"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"def involution(dw):\n",
" return dw.reverse().to_binary_tree_tamari().left_right_symmetry().to_dyck_word_tamari().reverse()"
]
},
{
"cell_type": "code",
"execution_count": 18,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 18,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 3\n",
"all(contact_partition(dw) == rise_partition(involution(dw)) for dw in DyckWords(n))"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Statistics on Tamari intervals"
]
},
{
"cell_type": "code",
"execution_count": 20,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"13\n"
]
},
{
"data": {
"text/plain": [
"[([1, 0, 1, 0, 1, 0], [1, 1, 1, 0, 0, 0]),\n",
" ([1, 0, 1, 1, 0, 0], [1, 1, 1, 0, 0, 0]),\n",
" ([1, 0, 1, 0, 1, 0], [1, 1, 0, 1, 0, 0]),\n",
" ([1, 0, 1, 0, 1, 0], [1, 1, 0, 0, 1, 0]),\n",
" ([1, 1, 0, 0, 1, 0], [1, 1, 1, 0, 0, 0]),\n",
" ([1, 1, 1, 0, 0, 0], [1, 1, 1, 0, 0, 0]),\n",
" ([1, 1, 0, 1, 0, 0], [1, 1, 1, 0, 0, 0]),\n",
" ([1, 1, 0, 0, 1, 0], [1, 1, 0, 1, 0, 0]),\n",
" ([1, 1, 0, 1, 0, 0], [1, 1, 0, 1, 0, 0]),\n",
" ([1, 1, 0, 0, 1, 0], [1, 1, 0, 0, 1, 0]),\n",
" ([1, 0, 1, 0, 1, 0], [1, 0, 1, 1, 0, 0]),\n",
" ([1, 0, 1, 1, 0, 0], [1, 0, 1, 1, 0, 0]),\n",
" ([1, 0, 1, 0, 1, 0], [1, 0, 1, 0, 1, 0])]"
]
},
"execution_count": 20,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"TIP3 = TamariIntervalPosets(3)\n",
"print(TIP3.cardinality())\n",
"[(tip.lower_dyck_word(), tip.upper_dyck_word()) for tip in TIP3]"
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {},
"outputs": [],
"source": [
"def contacts_interval(tip):\n",
" return tip.lower_dyck_word().number_of_touch_points()\n",
"\n",
"def rises_interval(tip):\n",
" return tip.upper_dyck_word().number_of_initial_rises()\n",
"\n",
"def contact_vector_interval(tip):\n",
" return contact_vector(tip.lower_dyck_word())\n",
"\n",
"def rise_vector_interval(tip):\n",
" return rise_vector(tip.upper_dyck_word())\n",
"\n",
"def contact_partition_interval(tip):\n",
" return contact_partition(tip.lower_dyck_word())\n",
"\n",
"def rise_partition_interval(tip):\n",
" return rise_partition(tip.upper_dyck_word())"
]
},
{
"cell_type": "code",
"execution_count": 31,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"tip = TamariIntervalPoset(10, [(2,5), (3,4), (4,5), (6,7), (8,10), (9,10), (3,2), (4,2), (6,5), (7,5), (8,5), (10,5), (9,8)])"
]
},
{
"cell_type": "code",
"execution_count": 32,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0]"
]
},
"execution_count": 32,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tip.lower_dyck_word()"
]
},
{
"cell_type": "code",
"execution_count": 33,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viewLatex(tip.lower_dyck_word())"
]
},
{
"cell_type": "code",
"execution_count": 34,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0]"
]
},
"execution_count": 34,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"tip.upper_dyck_word()"
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viewLatex(tip.upper_dyck_word())"
]
},
{
"cell_type": "code",
"execution_count": 27,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"text/plain": [
"[3, 0, 2, 0, 0, 4, 0, 0, 1, 0]"
]
},
"execution_count": 27,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"contact_vector_interval(tip)"
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[4, 3, 2, 1, 0, 0, 0, 0, 0, 0]"
]
},
"execution_count": 35,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"contact_partition_interval(tip)"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[3, 1, 0, 2, 3, 0, 1, 0, 0, 0]"
]
},
"execution_count": 36,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rise_vector_interval(tip)"
]
},
{
"cell_type": "code",
"execution_count": 37,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[3, 3, 2, 1, 1, 0, 0, 0, 0, 0]"
]
},
"execution_count": 37,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"rise_partition_interval(tip)"
]
},
{
"cell_type": "code",
"execution_count": 38,
"metadata": {
"slideshow": {
"slide_type": "-"
}
},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 38,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 3\n",
"sorted([[contact_partition_interval(tip), rise_partition_interval(tip)] for tip in TamariIntervalPosets(n)]) == \\\n",
"sorted([[rise_partition_interval(tip), contact_partition_interval(tip)] for tip in TamariIntervalPosets(n)])"
]
},
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"## Tamari Interval-Posets"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {},
"outputs": [],
"source": [
"tip = TamariIntervalPoset(10, [(2,5), (3,4), (4,5), (6,7), (8,10), (9,10), (3,2), (4,2), (6,5), (7,5), (8,5), (10,5), (9,8)])"
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viewLatex(tip)"
]
},
{
"cell_type": "code",
"execution_count": 41,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"([1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 0, 1, 0, 0],\n",
" [1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0])"
]
},
"execution_count": 41,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"(tip.lower_dyck_word(), tip.upper_dyck_word())"
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"def dc(tip):\n",
" L = [len(tip.decreasing_children(i)) for i in tip]\n",
" return [len(tip.decreasing_roots())] + L[:-1]\n",
"\n",
"def ic(tip):\n",
" L = [len(tip.increasing_children(i)) for i in tip]\n",
" L.reverse()\n",
" return [len(tip.increasing_roots())] + L[:-1]"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[3, 0, 2, 0, 0, 4, 0, 0, 1, 0]\n",
"[4, 2, 0, 0, 1, 0, 2, 1, 0, 0]\n"
]
}
],
"source": [
"print (dc(tip))\n",
"print (ic(tip))"
]
},
{
"cell_type": "code",
"execution_count": 44,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gt = tip.grafting_tree()\n",
"viewLatex(gt)"
]
},
{
"cell_type": "code",
"execution_count": 45,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gt_im = gt.left_border_symmetry()\n",
"viewLatex(gt_im)"
]
},
{
"cell_type": "code",
"execution_count": 46,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [],
"source": [
"tip2 = TamariIntervalPosets.from_grafting_tree(gt_im)"
]
},
{
"cell_type": "code",
"execution_count": 47,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viewLatex(tip2)"
]
},
{
"cell_type": "code",
"execution_count": 48,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[3, 0, 4, 0, 0, 1, 0, 0, 2, 0]\n",
"[3, 1, 0, 2, 3, 0, 1, 0, 0, 0]\n"
]
}
],
"source": [
"print (dc(tip2))\n",
"print (ic(tip2))"
]
},
{
"cell_type": "code",
"execution_count": 49,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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BYDAYzJB2mQjLlDnNj9aPDjF7Zq2R1w1porqKrSqsNY7dPZSPk5tsAw89WmvU/coSES0icCxLa41hnY3JPcdBp6HEXYNZPj645I2DxuGsEcmG43jaDE40HjTyeP7LlPXL9Ni/KAWVpl0DYKLxqpF3l4d3L660YHEsq9CtDmHfFNJsaEZ3hzi2G2VBT8lZTu1H/dQVVvh+IjdJVbbJ2b502QxWUS0iQB33Rek2js3GWcP2uKt7ZLUFfdj2/bfvoz9lBWPbIjN4/MPD+XfN5lhmB5PHhpbvT398+9nh8Q/vrq+wpDnSDHBNWouvX5wsfv+T7ydxK4tntEALtEALK4unX50sHkGzzOfi65vZB8mzuXj8/Mn3M7qdxQLjRT4p846cMN4Pv/0EbUiW24vFZEjP21hsL0YYj68ffD89szz/Mt92Lmsi0VhuO0cY5ONn30/P0YK3zRBqcF5Hxhjk9x++n6CbBXcDKtDgvaZOMCAVhWfBfzXhanD3LyYYgIrCtRC8tHI0+PtaUwwwReFbiPYzFhqC/c4ZBpCiCCyEO10zDdE++AwDRlFEFuI90ImG8HhkjgGhKEILye74SEN8bLbACL8oYgvZsclFQ3KcusAIvigSC+mB2qAhO2ZfYgReFJmF/Ki105C+f8HBCLooUgvFIfxJQ/5eDgcj5KLILVTvZ7z9Wf6+Fg8j3KIoLFQYD/+Uv8fHxQi1KCoLBcapI//6i+zhXIxAi6K0kGN02wvpuz18jCCLoraQYgzbTpmGACPAomhYyDAuryMSDQFGeEXRsZBgjF5TxRoijNCKomUhxpjsXwg1hBhhFUXPQogx29cSaQgxgiqKpoUIY7HfKdAQYwRUFF0LAQZnH5yvIcEIpijaFnwM7vEIV0OCEUpR9C24GIJjM56GDCOMohhY8DCEx6kcDSlGCEUxseBgSI7ZlxpSjACKYmSxxJC+f7HQkGN4L4qZxQJDcV7OXEOB4bkohhZzDOU5SjMNBYbfophazDA0zteaaqgwfBbF2GKKoXXu2kRDieGvKOYWk8VBNM/jG2soMbwVxcZiFO1zGkcaagxPRVnLYqyhgeGlKOtZjDQ0MHwUZU2Lq4YOxvpFWdfioqGFce+i0H3Z7I6by5+/G1uUOaXXa6l+GJ8P3mtoYdy9KEV74+HxlWFPhnNB64o0xeUf+GB8fm+noYdx96IUtCj2DhdDZe0Fh3uXNR9aDU2Mu7+iOF5Y22zba1GrfOekoYlx/1cUR409c3A4a+hi3P8VpWgvWHZ4OCMV3Tst+PD2V12M++96FTQrs9r6P5ixbE+q2uWS1H//TRNjhV0v2m5B6fb6v2u05MNJo91uOKySQB7/83dNjLV2vXYsv/z+o0aur6LDsij2qxw8fv7vP3T/6lrHKNbrAA1L5tS2K2CcNqD/011l9f5F2W+a0ZMyz8Bgu2RX+2qivebs/Yty6J+G9WzkTrPRvbTqaqxQlLx7NdhZ70sOK5fZbTf6/QxdjRUO5stuWZPNwXrfvM6vJlYY2hprvKJktCzz2n73aVfT8mi1BMZ5D1RTY51XlCqjbjvXlktgXHbHNTX8f+B4x1yPTTQ1fH/guA6GpkYIn8yvgKGpEXFRJofwehrxFmX6foaWRrxFmb25o6UBpijfDG/LMH+nS0sDTFGeXpwwtDTgFMVMY/keqI4GmKKYaXDeENbRAFMUIw3eu+MaGnCKYqLB/ahAQwNOUQw0+J+baGjAKYq+huBDJLUGoKJoa4g+UVNrACqKrobw40W1BqCiaGqIP2tVakAqip6G5INnpQakomhpyD6FV2pAKoqOhvSUBJUGqKJoaMjPz1BpgCqKWkNxsopKA1RRlBqqM3cUGrCKotJQnsak0IBVFIWG+pwuhQasosg1NE5wk2sAK4pUQ+dsP7kGsKLINLROfZRrACuKREPvPFD5SjXAiiLW0DwpVqoBrShCDd0zhKUa0Ioi0tA+XVq6ihG0ogg0tDGkGuCKwtfQx5BqgCsKV8MAQ7rCFbii8DRMMGQa8IrC0TDCkGnAK8pSwwxDtvoZvKIsNAwxJBoAizLXMMWQaAAsCvkyuRuMMYZkZTyARZnlnSmGWANiUWZ5b4oh1oBYFOcIV02EXxSLiDQiKIpFRBpJFkW4oibAolR11t0burS/xkWgAbEoJRtiv8iCQANiUWhOu9T2/4RgtVWARSHDNdaOK05wArEopL/Wce9yQ3i+BsSi9Klyl0fzV+KFWJQ+hdv6GzwNkEXpUm6cHs7VgFuUwmUtEsEqzWCLsnNYikSkAbco1Ha1iiE8DcBFub0G3KLYr2QyhKMBtyj30IBbFMK2bo/nrO4OtyjkeHR7/FIDcFGcs9QAXBTnLFf+B1wU5yw0Ui7KUiPloizvCpFyURYaSRdloZF0URZ3DEm6KHONtIsy10i7KPO7yaRdlJlG4kWZaSRelNmdhhIvylQj9aJMNVIvyvQuVKkXZaKRfFEmGskXZXKHsuSLMtbAoow1sCjju9dhUUYaWJSxBhZlfGdDLMpIA4tCRhpYFDK66yUWhVw1sChtzhpYlDbnO6JiUdoMGliULoMGFqXLcLdcLEqXXgOL0qfXwKL06e+kjEXp02lgUYZ0GliUId1Nzn88+P4xMBgMBoPBRJuS0tztetqIQtv1CPZuF1tHk2E9AserrWMJ7TWo/couMWXfX3WOW44uzZbRhmRO63dElGzLDtiTS9pFoTY2d3CPMdmm2Z/Gw2lxl2hyLE5fmg0rfP8gQeTQL2SSM+zKKcPyDA1zWC8snmx7hcZxmYZIQvsjFOqyelpEocWxLHGH45wmoxluQjEYDAaDwWAwGAwGg8FgMBgMBoPBYDAYDAaDwWAwGAwGg8FgMBgMBoPBYDA+kp0vOC9zSh3vUgs8lG7YcM1TVjeEbJK+/LzckUGjYlX3tfT9I/nNoEH760jrxNc0GTQO/ZXWReKXkQ4aw3XnReIXXM810t5w9Bolaow0doPGBjW6X1CjY5htN3z/PH4zaNSH7pfi4Pvn8ZvL3lf30rpNe22CatBotu3R23Gb8uI/RXFgrCja5Ux2h5KUB1zeZch52Yr/Az4ju8x2eMowAAAAJXRFWHRkYXRlOmNyZWF0ZQAyMDIwLTA2LTE2VDE1OjAxOjE1KzAyOjAwHg4RrwAAACV0RVh0ZGF0ZTptb2RpZnkAMjAyMC0wNi0xNlQxNTowMToxNSswMjowMG9TqRMAAAAUdEVYdHBkZjpWZXJzaW9uAFBERi0xLjUgBVwLOQAAAABJRU5ErkJggg==\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tip3 = tip2.complement()\n",
"viewLatex(tip3)"
]
},
{
"cell_type": "code",
"execution_count": 50,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gt = tip3.grafting_tree()\n",
"viewLatex(gt)"
]
},
{
"cell_type": "code",
"execution_count": 51,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gt_im = gt.left_border_symmetry()\n",
"viewLatex(gt_im)"
]
},
{
"cell_type": "code",
"execution_count": 52,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"tip_im = TamariIntervalPosets.from_grafting_tree(gt_im)\n",
"viewLatex(tip_im)"
]
},
{
"cell_type": "code",
"execution_count": 53,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[3, 3, 2, 1, 1, 0, 0, 0, 0, 0]\n",
"[4, 3, 2, 1, 0, 0, 0, 0, 0, 0]\n"
]
}
],
"source": [
"print (contact_partition_interval(tip_im))\n",
"print (rise_partition_interval(tip_im))"
]
},
{
"cell_type": "code",
"execution_count": 54,
"metadata": {
"slideshow": {
"slide_type": "subslide"
}
},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<IPython.core.display.Image object>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"viewLatex(tip.rise_contact_involution())"
]
},
{
"cell_type": "code",
"execution_count": 55,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"True"
]
},
"execution_count": 55,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"n = 3\n",
"all(contact_partition_interval(tip) == rise_partition_interval(tip.rise_contact_involution()) for tip in TamariIntervalPosets(n))"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {