An insertion algorithm for catabolizability

Details An insertion algorithm for catabolizability An insertion algorithm for catabolizability

2009-08-13

arxiv.org/abs/0908.1967v1

Mathematics

Combinatorics

12 pages, youngtab.sty for Young tableaux

Scientific paper

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}.

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