An explicit 1-factorization in the middle of the boolean lattice

D. A. Duffus, Henry Kierstead, H. S. Snevily

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Abstract

An explicit definition of a 1-factorization of Bk (the bipartite graph defined by the k- and (k + 1)-element subsets of [2k + 1]), whose constituent matchings are defined using addition modulo k + 1, is introduced. We show that the matchings are invariant under rotation (mapping under σ = (1, 2, 3, ..., 2k + 1)), describe the effect of reflection (mapping under p = (1, 2k + 1)(2, 2k)...(k, k + 2)), determine that there are no other symmetries which map these matchings among themselves, and prove that they are distinct from the lexical matchings in Bk.

Original languageEnglish (US)
Pages (from-to)334-342
Number of pages9
JournalJournal of Combinatorial Theory, Series A
Volume65
Issue number2
DOIs
StatePublished - Feb 1994

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ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics
  • Computational Theory and Mathematics

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