Proof of a conjectured q,t-Schr\"{o}der identity

TL;DR

This paper proves a conjecture related to the q,t-Schr"{o}der identity by combinatorially matching tableaux to Catalan words, preserving key statistical differences.

Contribution

It provides the first combinatorial proof of a specific limiting case of the q,t-Schr"{o}der theorem, confirming a conjecture by Chunwei Song.

Findings

Confirmed the conjecture through combinatorial methods

Established a tableau-Catalan word correspondence preserving the maj statistic

Enhanced understanding of q,t-Schr"{o}der identities

Abstract

A conjecture of Chunwei Song on a limiting case of the q,t-Schr\"{o}der theorem is proved combinatorially. The proof matches pairs of tableaux to Catalan words in a manner that preserves differences in the maj statistic.