Block-connected set partitions

Toufik Mansour; Augustine O. Munagi

doi:10.1016/j.ejc.2009.07.001

Block-connected set partitions

Toufik Mansour, Augustine O. Munagi

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

This paper introduces two statistics on set partitions, namely connector and circular connector. If B₁ / ... / B_k is a partition of {1, ..., n} with k > 1 blocks, then a connector is an ordered pair (c, c + 1) satisfying c ∈ B_i, c + 1 ∈ B_{i + 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 language	English
Pages (from-to)	887-902
Number of pages	16
Journal	European Journal of Combinatorics
Volume	31
Issue number	3
DOIs	https://doi.org/10.1016/j.ejc.2009.07.001
State	Published - Apr 2010

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2009.07.001

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Block-connected set partitions

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