Hook-content formula using excited Young diagrams

TL;DR

This paper introduces a new hook-content formula and its q-analog using excited Young diagrams, extending Naruse's hook-length formula for skew shapes, and explores their properties and conjectures.

Contribution

It presents a novel hook-content formula and q-analog based on excited Young diagrams, providing simple factorizations and raising new conjectures.

Findings

Hook-content formula constructed for skew shapes

Q-analog developed with simple factorization

Conjectures proposed for further exploration

Abstract

We construct a hook-content formula and its $q$-analog using excited Young diagrams analogous to Naruse's hook-length formula for skew shapes. Furthermore, we show that our hook-content formula has a simple factorization and give some conjectures and questions related to its $q$-analog.