An insertion algorithm for catabolizability

2009/08/13 by Jonah Blasiak, Blasiak, Jonah · 1 citation
Mathematics · #05E10 #Advanced Combinatorial Mathematics #Combinatorics (math.CO) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.0908.1967

openalex publication_date 2009/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Motivated by our recent work relating canonical bases to combinatorics of Garsia-Procesi modules \citeB, 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 \citeSW.

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