On Hook Formulas for Cylindric Skew Diagrams

TL;DR

This paper proposes a conjectural hook formula for counting standard tableaux on cylindric skew diagrams, extending Naruse's hook formula, and proves it in certain special cases.

Contribution

It introduces a new conjectural hook formula for cylindric skew diagrams and verifies it in specific instances, expanding the scope of hook formulas.

Findings

Conjectural hook formula for cylindric skew diagrams.

Proof of the formula in some special cases.

Extension of Naruse's hook formula.

Abstract

We present a conjectual hook formula concerning the number of the standard tableaux on "cylindric" skew diagrams. Our formula can be seen as an extension of Naruse's hook formula for skew diagrams. Moreover, we prove our conjecture in some special cases.