Polynomial Approach to Explicit Formulae for Generalized Binomial Coefficients

TL;DR

This paper extends a polynomial method to derive explicit formulas for generalized binomial coefficients and related combinatorial quantities, including path counts in Young graphs of strict partitions.

Contribution

It introduces a polynomial approach to new combinatorial problems, expanding previous methods to broader classes of formulas and structures.

Findings

Derived explicit formulas for generalized binomial coefficients.

Extended polynomial approach to path counting in Young graphs of strict partitions.

Demonstrated the method's applicability to multiple combinatorial problems.

Abstract

We extend the polynomial approach to hook length formula proposed in a recent joint paper with K\'arolyi, Nagy and Volkov to several other problems of the same type, including number of paths formula in the Young graph of strict partitions.