PreprintarXiv licencearXiv
Rectangular Symmetry for Catalan Functions
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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BibTeX
@misc{choi2026rectangular,
title = {{Rectangular Symmetry for Catalan Functions}},
author = {Hyeonjae Choi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.21535},
eprint = {2610.21535},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.21535},
}
RIS
TY - UNPB
TI - Rectangular Symmetry for Catalan Functions
AU - Hyeonjae Choi
PY - 2026
DA - 2026/10/15
PB - arXiv
DO - 10.48550/arxiv.2610.21535
UR - https://arxiv.org/abs/2610.21535
AB - 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.
ER -