A bijective proof of Andrews' refinement of the Alladi-Schur theorem

TL;DR

This paper presents a bijective proof of Andrews' refinement of the Alladi-Schur theorem and shows how this framework can reproduce Andrews' recursive relations for the polynomials.

Contribution

It introduces a new bijective proof technique for a refined partition theorem and extends it to recursive relations of related polynomials.

Findings

Bijective proof of Andrews' refinement of the Alladi-Schur theorem

Framework reproduces Andrews' recursive relations for Alladi-Schur polynomials

Provides a new combinatorial perspective on partition identities

Abstract

This paper gives a bijective proof of Andrews' refinement of the Alladi-Schur theorem. Moreover, it demonstrates that the bijective framework introduced here can be used to reproduce and provide a bijective account of Andrews' recursive relations for the Alladi-Schur polynomials.