Signed Hypergraph Designs and Diagonal Forms for Some IncidenceMatrices

Authors:
Richard M. Wilson
Affiliations:
Dept. of Mathematics, 253-37, California Institute of Technology, Pasadena, CA 91125
Venue:
Designs, Codes and Cryptography - Special issue on designs and codes—a memorial tribute to Ed Assmus
Year:
1999

Citing 4
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Diagonal forms of incidence matrices associated with t-uniform hypergraphs

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Abstract

Givena t-uniform hypergraph H on kvertices and an assignment of integers f(T) to thet-subsets T of a v-setX, v\ge k+t, e give necessary andsufficient conditions for the existence of an assignment of integermultiplicities h(G) to those subhypergraphs Gof the complete t-uniform hypergraph on vvertices that are isomorphic to H so that the sumof the integers h(G) over those G thatcontain T is f(T). Our main theoremis stated in terms of integral matrices. As a consequence ofour main theorem, e also determine a diagonal form, and hencethe p-rank for all primes p, for theincidence matrix of t-subsets versus subhypergraphsisomorphic to H.