The contributions of Stanley to the fabric of symmetric and quasisymmetric functions

TL;DR

This paper explores Richard Stanley's foundational work on symmetric and quasisymmetric functions, highlighting their significance in combinatorics and how they facilitate counting combinatorial objects.

Contribution

It synthesizes Stanley's contributions to the theory of symmetric and quasisymmetric functions, emphasizing their role in combinatorial enumeration.

Findings

Symmetric and quasisymmetric functions are central to combinatorial counting.

Stanley's work established key properties and applications of these functions.

The paper underscores the importance of these functions in understanding combinatorial structures.

Abstract

We weave together a tale of two rings, SYM and QSYM, following one gold thread spun by Richard Stanley. The lesson we learn from this tale is that "Combinatorial objects like to be counted by quasisymmetric functions."