Cyclic compositions and cycles of the hypercube


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 \(Q_n\).

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Correspondence to N. Zagaglia Salvi.

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Ferrari, M.M., Salvi, N.Z. Cyclic compositions and cycles of the hypercube. Aequat. Math. 92, 671–682 (2018).

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

Mathematics Subject Classification

  • Primary 05A17
  • Secondary 05C38