TY - JOUR

T1 - An explicit 1-factorization in the middle of the boolean lattice

AU - Duffus, D. A.

AU - Kierstead, Henry

AU - Snevily, H. S.

N1 - Funding Information:
For a fixed k, denote the collection of j-element subsets of \[2k + 1\] = { 1, 2 ..... 2k + 1 } by Rj and let B k be the bipartite graph defined on the vertex set Rk ~ Rk+ 1 by letting A be adjacent to B iff A c B or vice versa. In \[KT\] the second author and Trotter introduced an explicit 1-factorization {1o ..... lk} of Bk, called the lexical factorization, and determined its behavior under the automorphisms of Bk. In this article we report on * Supported by Office of Naval Research Grant N0004-85-K-0769. * Supported by Office of Naval Research Grant N00014-90-J-1206.

PY - 1994/2

Y1 - 1994/2

N2 - 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.

AB - 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.

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U2 - 10.1016/0097-3165(94)90030-2

DO - 10.1016/0097-3165(94)90030-2

M3 - Article

AN - SCOPUS:38149146911

VL - 65

SP - 334

EP - 342

JO - Journal of Combinatorial Theory - Series A

JF - Journal of Combinatorial Theory - Series A

SN - 0097-3165

IS - 2

ER -