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arXiv · 2004.04937

Modular and fractional L-intersecting families of vector spaces

Rogers Mathew·Tapas Kumar Mishra·Ritabrata Ray·Shashank Srivastava
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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 \emph{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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Rogers Mathew, Tapas Kumar Mishra, Ritabrata Ray, Shashank Srivastava. 2020-04-10. Modular and fractional L-intersecting families of vector spaces. https://arxiv.org/abs/2004.04937

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