Generating functions from the viewpoint of Rota-Baxter algebras

Nancy S.S. Gu, Li Guo

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We study generating functions in the context of Rota-Baxter algebras. We show that exponential generating functions can be naturally viewed as a very special case of complete free commutative Rota-Baxter algebras. This viewpoint allows us to apply free Rota-Baxter algebras to give a large class of algebraic structures in which generalizations of generating functions can be studied. We generalize the product formula and composition formula for exponential power series. We also give generating functions both for known number families such as Stirling numbers of the second kind and partition numbers, and for new number families such as those from not necessarily disjoint partitions and partitions of multisets.

Original languageEnglish (US)
Pages (from-to)536-554
Number of pages19
JournalDiscrete Mathematics
Volume338
Issue number4
DOIs
StatePublished - Apr 6 2015

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

Keywords

  • Generating function
  • Partition
  • Rota-Baxter algebra
  • Stirling number

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