Block-connected set partitions

Toufik Mansour, Augustine O. Munagi

Research output: Contribution to journalArticlepeer-review


This paper introduces two statistics on set partitions, namely connector and circular connector. If B1 / ... / Bk is a partition of {1, ..., n} with k > 1 blocks, then a connector is an ordered pair (c, c + 1) satisfying c ∈ Bi, c + 1 ∈ Bi + 1, i = 1, ..., n - 1. A circular connector is a connector when the blocks of a partition are arranged on a circle. We concentrate on the enumeration of partitions according to the two statistics, and certain variations thereof. Our results include several nice generating functions and explicit formulas. We also establish connections between connected partitions and words over a finite alphabet, and random walks on a square lattice.

Original languageEnglish
Pages (from-to)887-902
Number of pages16
JournalEuropean Journal of Combinatorics
Issue number3
StatePublished - Apr 2010

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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