Opened 4 years ago
Closed 4 years ago
#24560 closed enhancement (fixed)
direct access to mTamari lattices
Reported by:  chapoton  Owned by:  

Priority:  major  Milestone:  sage8.2 
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: 
Description
that are currently somewhat hidden
Change History (12)
comment:1 Changed 4 years ago by
 Branch set to u/chapoton/24560
 Commit set to 7406b309e697faf79583345463cec6ebe75ad4e4
 Status changed from new to needs_review
comment:3 Changed 4 years ago by
Well, a=m*n+1 and b=n in the case of interest here
comment:4 followup: ↓ 5 Changed 4 years ago by
Oops, I derped. Looks good. But:
 In the class doc of
GeneralizedTamariLattice
, I'd replacea \geq b \times m
bya \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
Replying to darij:
Oops, I derped. Looks good. But:
 In the class doc of
GeneralizedTamariLattice
, I'd replacea \geq b \times m
bya \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
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
Of course, the mTamari 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 PrevilleRatelle and Viennot, because shape and slope become independant parameters.
comment:8 Changed 4 years ago by
 Commit changed from 7406b309e697faf79583345463cec6ebe75ad4e4 to 2b614588ac014d88bf4592a5a2411a500df54c04
Branch pushed to git repo; I updated commit sha1. New commits:
2b61458  one detail about times

comment:9 Changed 4 years ago by
Ah, they aren't cornertocorner paths...
comment:10 Changed 4 years ago by
 Reviewers set to Darij Grinberg
 Status changed from needs_review to positive_review
comment:11 Changed 4 years ago by
Thanks
comment:12 Changed 4 years ago by
 Branch changed from u/chapoton/24560 to 2b614588ac014d88bf4592a5a2411a500df54c04
 Resolution set to fixed
 Status changed from positive_review to closed
New commits:
allow easy access to mTamari lattices