Modular and fractional L-intersecting families of vector spaces

04/10/2020

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by   Rogers Mathew, et al.

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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]. This is 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.