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Journal article
An insertion algorithm for catabolizability
European journal of combinatorics, v 33(2), pp 267-276
01 Feb 2012
Abstract
Our recent work in Blasiak (2011)
[1] exhibits a canonical basis of the Garsia–Procesi module
R
λ
with cells labeled by standard tableaux of catabolizability
⊵
λ
. Through our study of the Kazhdan–Lusztig preorder on this basis, we found a way to transform a standard word labeling a basis element into a word inserting to the unique tableau of shape
λ
. This led to an algorithm that computes the catabolizability of the insertion tableau of a standard word. We deduce from this a characterization of catabolizability as the statistic on words invariant under Knuth transformations, certain (co)rotations, and a new set of transformations we call catabolism transformations. We further deduce a Greene’s Theorem-like characterization of catabolizability and a result about how cocyclage changes catabolizability, strengthening a similar result in Shimozono and Weyman (2000)
[8].
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Details
- Title
- An insertion algorithm for catabolizability
- Creators
- Jonah Blasiak - University of California, Berkeley
- Publication Details
- European journal of combinatorics, v 33(2), pp 267-276
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000297890300015
- Scopus ID
- 2-s2.0-80155211163
- Other Identifier
- 991021862386804721
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- Mathematics