Journal article

THE EXISTENCE OF NONTRIVIAL HYPERFACTORIZATIONS OF K2N


Authors listBOROS, E; JUNGNICKEL, D; VANSTONE, SA

Publication year1991

Pages9-15

JournalCombinatorica

Volume number11

Issue number1

ISSN0209-9683

DOI Linkhttps://doi.org/10.1007/BF01375468

PublisherSpringer


Abstract

A lambda-hyperfactorization of K2n is a collection of 1-factors of K2n for which each pair of disjoint edges appears in precisely-lambda of the 1-factors. We call a lambda-hyperfactorization trivial if it contains each 1-factor of K2n with the same multiplicity-gamma (then lambda = gamma(2n - 5)!!). A lambda-hyperfactorization is called simple if each 1-factor of K2n appears at most once. Prior to this paper, the only known non-trivial lambda-hyperfactorizations had one of the following parameters (or were multipliers of such an example) (i) 2n = 2a + 2, lambda = 1 (for all a greater-than-or-equal-to 3); cf. Cameron [3]; (ii) 2n = 12, lambda = 15 or 2n = 24, lambda = 495; cf. Jungnickel and Vanstone [8].

In the present paper we show the existence of non-trivial simple lambda-hyperfactorizations of K2n for all n greater-than-or-equal-to 5.




Citation Styles

Harvard Citation styleBOROS, E., JUNGNICKEL, D. and VANSTONE, S. (1991) THE EXISTENCE OF NONTRIVIAL HYPERFACTORIZATIONS OF K2N, Combinatorica, 11(1), pp. 9-15. https://doi.org/10.1007/BF01375468

APA Citation styleBOROS, E., JUNGNICKEL, D., & VANSTONE, S. (1991). THE EXISTENCE OF NONTRIVIAL HYPERFACTORIZATIONS OF K2N. Combinatorica. 11(1), 9-15. https://doi.org/10.1007/BF01375468



Keywords


5-DESIGNS

Last updated on 2025-02-04 at 07:39