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Aequationes mathematicae

, Volume 92, Issue 4, pp 671–682 | Cite as

Cyclic compositions and cycles of the hypercube

  • M. M. Ferrari
  • N. Zagaglia Salvi
Article
  • 43 Downloads

Abstract

The partition graph of a positive integer n, \(P_n\), is the graph whose vertices are the cyclic compositions of n and two vertices are adjacent if one composition is obtained from the other one by replacing two cyclically consecutive parts by their sum. In this paper we introduce and investigate the notions of singular cyclic composition and singular edge of \(P_n\). We associate with every singular edge and every cycle of \(P_n\), whose vertices are aperiodic cyclic compositions of n, a cycle or a set of disjoint cycles of equal length of the hypercube \(Q_n\).

Keywords

Composition Cyclic composition Singular composition Singular cyclic composition Partition graph Hypercube Necklace Quotient of the Boolean lattice 

Mathematics Subject Classification

Primary 05A17 Secondary 05C38 

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South FloridaTampaUSA
  2. 2.Dipartimento di MatematicaPolitecnico di MilanoMilanoItaly

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