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arXiv · 0908.1967

An insertion algorithm for catabolizability

Jonah Blasiak
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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}.

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Jonah Blasiak. 2009-08-13. An insertion algorithm for catabolizability. https://arxiv.org/abs/0908.1967

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