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.
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics