PreprintarXiv licencearXiv
Anti-ribbon shaped Young diagram decomposition
Abstract
We introduce a sliding procedure on diagrams which splits the standard Young tableaux of a corner-crossed diagram, in particular of a skew shape, along a finite binary tree whose leaves are anti-ribbon diagrams. Combined with standardization, this yields a decomposition of semi-standard Young tableaux into tableaux of anti-ribbon shape, indexed by standard tableaux and governed by their descent sets. As applications, we obtain expansions of Schur functions and Schur multiple zeta functions in terms of their anti-ribbon type analogues; at the level of Schur functions, this is a tableau-level form of Gessel's fundamental quasisymmetric expansion.
Related
- Temperley-Lieb Immanants of Ribbon Decomposition Matrices
- Minimal output entropy for the channels that add or remove a box of a Young diagram, and a Pauli principle for every permutation symmetry
- River ribbon tableaux and symmetric group characters
- Counting tangles in coverings of closed 2-orbifolds via ribbon categories
- Convex ribbon disks, quasipositivity, and Lagrangian sliceness
BibTeX
@misc{murahara2026antiribbon,
title = {{Anti-ribbon shaped Young diagram decomposition}},
author = {Hideki Murahara and Maki Nakasuji and Wataru Takeda},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.07715},
eprint = {2611.07715},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.07715},
}
RIS
TY - UNPB
TI - Anti-ribbon shaped Young diagram decomposition
AU - Hideki Murahara
AU - Maki Nakasuji
AU - Wataru Takeda
PY - 2026
DA - 2026/11/05
PB - arXiv
DO - 10.48550/arxiv.2611.07715
UR - https://arxiv.org/abs/2611.07715
AB - We introduce a sliding procedure on diagrams which splits the standard Young tableaux of a corner-crossed diagram, in particular of a skew shape, along a finite binary tree whose leaves are anti-ribbon diagrams. Combined with standardization, this yields a decomposition of semi-standard Young tableaux into tableaux of anti-ribbon shape, indexed by standard tableaux and governed by their descent sets. As applications, we obtain expansions of Schur functions and Schur multiple zeta functions in terms of their anti-ribbon type analogues; at the level of Schur functions, this is a tableau-level form of Gessel's fundamental quasisymmetric expansion.
ER -