Opened 4 years ago

Closed 4 years ago

#24560 closed enhancement (fixed)

direct access to m-Tamari lattices

Reported by: chapoton Owned by:
Priority: major Milestone: sage-8.2
Component: combinatorics Keywords:
Cc: tscrim, stumpc5, darij Merged in:
Authors: Frédéric Chapoton Reviewers: Darij Grinberg
Report Upstream: N/A Work issues:
Branch: 2b61458 (Commits, GitHub, GitLab) Commit: 2b614588ac014d88bf4592a5a2411a500df54c04
Dependencies: Stopgaps:

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Description

that are currently somewhat hidden

Change History (12)

comment:1 Changed 4 years ago by chapoton

  • Branch set to u/chapoton/24560
  • Commit set to 7406b309e697faf79583345463cec6ebe75ad4e4
  • Status changed from new to needs_review

New commits:

7406b30allow easy access to m-Tamari lattices

comment:2 Changed 4 years ago by darij

EDIT : --

Last edited 4 years ago by darij (previous) (diff)

comment:3 Changed 4 years ago by chapoton

Well, a=m*n+1 and b=n in the case of interest here

comment:4 follow-up: Changed 4 years ago by darij

Oops, I derped. Looks good. But:

  • In the class doc of GeneralizedTamariLattice, I'd replace a \geq b \times m by a \geq bm. The \times is misleading, as it makes me think of a rectangle.
  • Is the lattice property of a GeneralizedTamariLattice still a conjecture?

comment:5 in reply to: ↑ 4 Changed 4 years ago by chapoton

Replying to darij:

Oops, I derped. Looks good. But:

  • In the class doc of GeneralizedTamariLattice, I'd replace a \geq b \times m by a \geq bm. The \times is misleading, as it makes me think of a rectangle.

ok

  • Is the lattice property of a GeneralizedTamariLattice still a conjecture?

Well, I think so.

comment:6 Changed 4 years ago by darij

Actually, it seems to follow from https://arxiv.org/pdf/1406.3787.pdf , Theorem 1, doesn't it? (Where v is the Christoffel path, i.e., the (a,b)-Dyck path that keeps closest to the diagonal.)

comment:7 Changed 4 years ago by chapoton

Of course, the m-Tamari lattices themselves are known to be lattices.

In general no, and this is more subtle. In this sage procedure, the generalisation goes beyond that of Preville-Ratelle and Viennot, because shape and slope become independant parameters.

comment:8 Changed 4 years ago by git

  • Commit changed from 7406b309e697faf79583345463cec6ebe75ad4e4 to 2b614588ac014d88bf4592a5a2411a500df54c04

Branch pushed to git repo; I updated commit sha1. New commits:

2b61458one detail about times

comment:9 Changed 4 years ago by darij

Ah, they aren't corner-to-corner paths...

comment:10 Changed 4 years ago by darij

  • Reviewers set to Darij Grinberg
  • Status changed from needs_review to positive_review

comment:11 Changed 4 years ago by chapoton

Thanks

comment:12 Changed 4 years ago by vbraun

  • Branch changed from u/chapoton/24560 to 2b614588ac014d88bf4592a5a2411a500df54c04
  • Resolution set to fixed
  • Status changed from positive_review to closed
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