A Recursive Construction For Regular Difference Triangle Sets

Autor:	Solomon W. Golomb, Charles J. Colbourn, Wensong Chu
Rok vydání:	2005
Předmět:	Set (abstract data type) Discrete mathematics Combinatorics Combinatorial design Difference set Integer General Mathematics Order (ring theory) Monotonic function Type (model theory) Golomb ruler Mathematics
Zdroj:	SIAM Journal on Discrete Mathematics. 18:741-748
ISSN:	1095-7146 0895-4801
DOI:	10.1137/s0895480103436761
Popis:	A difference triangle set (D$\Delta$S) is a collection of sets of integers having the property that every integer can be written in at most one way as the difference of two elements within a set of the collection. The standard objective is to minimize the largest difference represented, given a specified size of the collection and sizes of the sets that it contains. In order to construct D$\Delta$Ss, we present a new type of combinatorial design, monotonic directed $(v,k,\lambda)$-designs (MDDs). Using MDDs, we give a general recursive construction for difference triangle sets (D$\Delta$Ss). Several instances of this main construction are derived. One of these, the perfect construction, leads to an infinite family of regular (optimal) D$\Delta$Ss if the existence of a single regular D$\Delta$S is known.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0d89997f73aedbd4bdcee6cc99249d1a https://doi.org/10.1137/s0895480103436761 Zobrazit plný text záznamu Plný text ve formátu PDF