Fix is_graded for Posets to use appropriate definition

[anneschilling]

Fix is_graded to use the following definition a poset is graded if all maximal chains have the same lengths. See Stanley, EC1.

As per this definition, the following poset is not graded:

    sage: P = Poset([[1,2,3,4], [[1,2],[2,4],[3,4]]])
    sage: P.is_graded()
    True

Beware that not everybody agree on this choice of definition for
ranked / graded. See http://en.wikipedia.org/wiki/Graded_poset.

See also: #12993 and #13223 for a followup!

CC: @sagetrac-sage-combinat

Component: combinatorics

Keywords: sd40, posets

Author: Franco Saliola

Reviewer: Anne Schilling

Merged: sage-5.2.beta1

Issue created by migration from https://trac.sagemath.org/ticket/13222

[nthiery]

Changed reviewer from Anne Schilling and SD40 to Anne Schilling, SD40

[anneschilling]

Changed keywords from sd40 to sd40, posets

[anneschilling]

Attachment: trac_13222_is_graded_for_posets.patch.gz

[anneschilling]

comment:7

This patch was written and reviewed during the tutorial session lead by Franco Saliola and Anne Schilling during Sage Days 40 with all participants.

Positive review.

[anneschilling]

comment:9

Positive review if all tests pass on Patchbot (only tested all Tests in /combinat/posets).

[jdemeyer]

comment:10

Not sure whether "SD40" as reviewer makes much sense, mind if I remove it?

[jdemeyer]

Changed reviewer from Anne Schilling, SD40 to Anne Schilling

[anneschilling]

comment:11

Replying to @jdemeyer:

Not sure whether "SD40" as reviewer makes much sense, mind if I remove it?

Sure. We wrote and sort of reviewed the patch during a tutorial at Sage Days 40, so I wanted to give everyone credit for it since many people gave input during the writing and reviewing.

Anne

[jdemeyer]

Merged: sage-5.2.beta1