|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Crystals & trees: quasi-Kashiwara operators, monoids of binary trees, and Robinson--Schensted-type correspondences | | Alan J. Cain
; António Malheiro
; | | Date: |
9 Feb 2017 | | Abstract: | Kashiwara’s crystal graphs have a natural monoid structure that arises by
identifying words labelling vertices that appear in the same position of
isomorphic components. The celebrated plactic monoid (the monoid of Young
tableaux), arises in this way from the crystal graph for the $q$-analogue of
the special linear Lie algebra $mathfrak{sl}_{n}$, and the so-called Kashiwara
operators interact beautifully with the combinatorics of Young tableaux and
with the Robinson--Schensted--Knuth correspondence. The authors previously
constructed an analogous ’quasi-crystal’ structure for the related hypoplactic
monoid (the monoid of quasi-ribbon tableaux), which has similarly neat
combinatorial properties. This paper constructs an analogous ’crystal-type’
structure for the sylvester and Baxter monoids (the monoids of binary search
trees and pairs of twin binary search trees, respectively). Both monoids are
shown to arise from this structure just as the plactic monoid does from the
usual crystal graph. The interaction of the structure with the sylvester and
Baxter versions of the Robinson--Schensted--Knuth correspondence is studied.
The structure is then applied to prove results on the number of factorizations
of elements of these monoids, and to prove that both monoids satisfy
non-trivial identities. | | Source: | arXiv, 1702.2998 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER