Year: 2025
Type: preprint
Abstract: What might a combinatorial interpretation of the Kronecker coefficients even look like? We introduce a class of combinatorial objects called bitableaux, which we believe are a natural candidate, and we formulate a purely combinatorial problem which if resolved would give a combinatorial interpretation of the Kronecker coefficients. We make some partial progress on this problem -- enough to extract a combinatorial expansion for a Kronecker product of Schur functions in the monomial basis. We also explain how in this framework finding a combinatorial interpretation for Kronecker coefficients can be thought of as looking for a generalization of the RSK and dual RSK insertion algorithms.
Source: arXiv (Cornell University)
Authors: Harman, Nate, Wilson, Alexander N.
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416834990
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