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
SN - 0097-3165
VL - 65
SP - 334
EP - 342
JO - Journal of Combinatorial Theory, Series A
JF - Journal of Combinatorial Theory, Series A
IS - 2
ER -