Unified generating function for set partitions

2022/08/25 by Orli Herscovici, Herscovici, Orli
Mathematics · #05A10 #05A15 #05A18 #05A30 #11B73 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Functional Equations Stability Results

paper · pdf · doi:10.48550/arxiv.2208.12325

openalex publication_date 2022/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this work we define a unified generating functions for 9 different kinds of set partitions including cyclically ordered set partitions. Such generating function depends on 4 parameters. We consider property of this function and provide combinatorial explanation for polynomials generated by this function. Two new combinatorial statistics are defined and the explicit formulae given for coefficients of parametrized polynomials defined by the generating function.

Related

• Proposal of a generating function of partition sequences
• Counting symmetric and non-symmetric peaks in a set partition
• A unified treatment of families of partition functions
• Stabilization of coefficients for partition polynomials
• Polynomials associated with Partitions: Polynomials associated with Partitions: Their Asymptotics and Zeros