Add "Standard example" poset

[jm58660]

As #19383 seems dead (and latest push do not merge anymore), I suggest adding standard example in it's own in this ticket.

It is logical to have StandardExample(n) to always have dimension n. This is not the case when n=1. Hence I added a restriction n >= 2.

CC: @fchapoton @tscrim @jhpalmieri

Component: combinatorics

Keywords: poset

Author: Kevin Dilks, Jori Mäntysalo

Branch/Commit: 7c74da6

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/19690

[jm58660]

Branch: u/jmantysalo/add__standard_example__poset

[jm58660]

Changed keywords from none to poset

[jm58660]

Author: Kevin Dilks, Jori Mäntysalo

[jm58660]

Changed branch from u/jmantysalo/add__standard_example__poset to none

[jm58660]

Commit: acd7169

[jm58660]

Branch: u/jmantysalo/add__standard_example__poset

[jm58660]

comment:4

Nathann, you already saw this in #19383, so I guess this is an easy review.

Documentation could be extended and said that Dedekind-Macneille completion of standard example is the Boolean lattice. (That is, this is also kind of standard example showing that completion by cuts can be exponential in size.) But then, doc can not say every mathematical fact.

[nathanncohen]

comment:5

It is, but I do not agree with the terminology and so I chose to not review it.

[jm58660]

comment:6

Replying to @nathanncohen:

It is, but I do not agree with the terminology and so I chose to not review it.

Duh. Travis?

[jm58660]

comment:7

About terminology: in issue 2/2015 of Order there is a paper titled "Standard Examples as Subposets of Posets". I just can not see what else the name of the poset should be.

[jm58660]

comment:8

John, if you are interested in names... What about this one?

[jhpalmieri]

comment:9

If the name seems to be widely accepted, okay, but add a reference.

[jm58660]

comment:10

Replying to @jhpalmieri:

If the name seems to be widely accepted, okay, but add a reference.

What kind of reference? Googling founds books "Handbook of Discrete and Combinatorial Mathematics" and "Introduction to Lattice Theory with Computer Science Applications" and there are many papers. And Wikipedia uses the term.

But what is more important, I have not seen this poset named as something else, and neither seen "standard poset" used to refer any other poset.

[jhpalmieri]

comment:11

I don't know why you are resistant to adding a reference; what harm can it possibly cause? Can't adding a reference only improve the situation? Anyway, you asked my opinion. At least one other person expressed the same opinion. Use wikipedia or use some other reference; I'm not a poset expert, so I don't know what reference would be most definitive.

[jm58660]

comment:12

Replying to @jhpalmieri:

I don't know why you are resistant to adding a reference; what harm can it possibly cause?

No no, I am not against. My question was not rhetorical, but I really asked what the reference should be.

[tscrim]

comment:13

I would add both references.

I made a few tweaks to the documentation. Once you add the references, you can set this to a positive review on my behalf (in part because I can't think of a better name at this point).

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New commits:

c2c7fa5	Merge branch 'u/jmantysalo/add__standard_example__poset' of trac.sagemath.org:sage into u/jmantysalo/add__standard_example__poset
6b4abd5	Some doctest and formatting tweaks.

[tscrim]

Changed branch from u/jmantysalo/add__standard_example__poset to u/tscrim/add_standard_example_poset-19690

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Changed commit from acd7169 to 6b4abd5

[jm58660]

Changed branch from u/tscrim/add_standard_example_poset-19690 to u/jmantysalo/add_standard_example_poset-19690

[jm58660]

Changed commit from 6b4abd5 to 7c74da6

[jm58660]

comment:15

Replying to @tscrim:

Once you add the references, you can set this to a positive review on my behalf

OK. Thanks.

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New commits:

7c74da6

References to standar example.

[vbraun]

Changed branch from u/jmantysalo/add_standard_example_poset-19690 to 7c74da6