TL;DR
The paper introduces shifted domino tableaux, establishes their bijection with shifted Young tableaux, and connects them to super shifted plactic monoids, providing new combinatorial interpretations of products of Q- and P-Schur functions.
Contribution
It presents the novel combinatorial objects called shifted domino tableaux and links them to shifted Young tableaux and super shifted plactic monoids, expanding the combinatorial framework for symmetric functions.
Findings
Shifted domino tableaux are in bijection with pairs of shifted Young tableaux.
Sum over shifted domino tableaux describes products of Q-Schur functions.
Different types of shifted domino tableaux describe products of P-Schur functions.
Abstract
We introduce new combinatorial objects called the shifted domino tableaux. We prove that these objects are in bijection with pairs of shifted Young tableaux. This bijection shows that shifted domino tableaux can be seen as elements of the super shifted plactic monoid, which is the shifted analog of the super plactic monoid. We also show that the sum over all shifted domino tableaux of a fixed shape describe a product of two Q-Schur functions, and by taking a different kind of shifted domino tableaux we describe a product of two P-Schur functions.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · semigroups and automata theory