Modular and fractional L-intersecting families of vector spaces

2020/04/10 by Mathew, Rogers, Mishra, Tapas Kumar, Ray, Ritabrata +1 · 1 citation
#05D05 #Combinatorics (math.CO) #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #FOS: Mathematics #G.2.1

paper · doi:10.48550/arxiv.2004.04937

Abstract

In the first part of this paper, we prove a theorem which is the q-analogue of a generalized modular Ray-Chaudhuri-Wilson Theorem shown in [Alon, Babai, Suzuki, J. Combin. Theory Series A, 1991]. It is also a generalization of the main theorem in [Frankl and Graham, European J. Combin. 1985] under certain circumstances. In the second part of this paper, we prove q-analogues of results on a recent notion called fractional L-intersecting family for families of subspaces of a given vector space. We use the above theorem to obtain a general upper bound to the cardinality of such families. We give an improvement to this general upper bound in certain special cases.

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• q-analogues of Fisher's inequality and oddtown theorem

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