An insertion algorithm for catabolizability
Combinatorics
2009-08-17 v1 Representation Theory
Abstract
Motivated by our recent work relating canonical bases to combinatorics of Garsia-Procesi modules \cite{B}, we give an insertion algorithm that computes the catabolizability of the insertion tableau of a standard word. This allows us to characterize catabolizability as the statistic on words invariant under Knuth transformations, certain (co)rotations, and a new operation called a catabolism transformation. We also prove a Greene's Theorem-like characterization of catabolizability, and a result about how cocyclage changes catabolizability, strengthening a similar result in \cite{SW}.
Cite
@article{arxiv.0908.1967,
title = {An insertion algorithm for catabolizability},
author = {Jonah Blasiak},
journal= {arXiv preprint arXiv:0908.1967},
year = {2009}
}
Comments
12 pages, youngtab.sty for Young tableaux