Enumeration of standard Young tableaux of certain truncated shapes

TL;DR

This paper discovers and proves new product formulas for counting standard Young tableaux of specific truncated shapes, including shifted staircase and rectangular shapes with a corner removed.

Contribution

It introduces novel enumeration formulas for standard Young tableaux of truncated shapes, expanding the combinatorial understanding of these objects.

Findings

Derived explicit product formulas for shifted staircase truncated shapes.

Established enumeration formulas for rectangular truncated shapes.

Extended known results to new classes of truncated shapes.

Abstract

Unexpected product formulas for the number of standard Young tableaux of certain truncated shapes are found and proved. These include shifted staircase shapes minus a square in the NE corner, rectangular shapes minus a square in the NE corner, and some variations.