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arXiv · 2610.21535

Rectangular Symmetry for Catalan Functions

Hyeonjae Choi
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Abstract

Katabolizable tableaux provide a combinatorial formula for the Schur coefficients of Catalan functions. We prove that a tableau involution preserves katabolizability under antidiagonal reflection of any upper root ideal. This involution complements shape and content in a fixed rectangle and preserves charge. We obtain a bijective proof of the rectangular symmetry of these coefficients.

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Hyeonjae Choi. 2026-10-15. Rectangular Symmetry for Catalan Functions. https://arxiv.org/abs/2610.21535

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