An insertion algorithm for catabolizability
Abstract
Motivated by our recent work relating canonical bases to combinatorics of Garsia-Procesi modules 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 SW.
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