A reciprocity relation for t-designs
type: Item
instance of: scholarly article
title: A reciprocity relation for t-designs
zbMATH Open document ID: 0659.05014
DOI: 10.1016/S0195-6698(87)80021-5
author: S. S. Shrikhande
author: N. M. Singhi
published in: European Journal of Combinatorics
publication date: 1987-01-01T00:00:00Z
review text: It is shown that for a given t, v, k, the monoid of all t-(v,k,\(\lambda)\) designs is a toroidal monoid in the sense of Hochester and Stanley and the corresponding monoid algebra is Gorenstein. Among the consequences deduced is the fact that the function \(P^ v_{k,t}(\lambda)=\) the number of distinct t-(v,k,\(\lambda)\) designs is quasi-periodic and satisfies a reciprocity relation. Some generalizations and related problems are discussed.
Mathematics Subject Classification ID: 05B05
zbMATH DE Number: 4077220
zbMATH Keywords: toroidal monoid
zbMATH Keywords: monoid algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4077220