Sign under the domino Robinson-Schensted maps

TL;DR

This paper extends a known permutation sign formula to a broader class of domino Robinson-Schensted algorithms, enhancing understanding of their combinatorial properties.

Contribution

It generalizes a classical permutation sign formula to a family of domino Robinson-Schensted algorithms, providing new insights into their combinatorial structure.

Findings

Generalization of sign formula to domino Robinson-Schensted maps

Enhanced understanding of permutation signs in domino algorithms

Potential applications in combinatorics and representation theory

Abstract

We generalize a formula obtained independently by A. Reifegerste and J. Sj\"ostrand for the sign of a permutation under the classical Robinson-Schensted map to a family of domino Robinson-Schensted algorithms.