Modular and fractional L-intersecting families of vector spaces

Mathew, R. and Kumar Mishra, Tapas and Ray, Ritabrata and Srivastava, Shashank (2022) Modular and fractional L-intersecting families of vector spaces. The Electronic Journal of Combinatorics, 29 (1). pp. 1-20. ISSN 1077-8926

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Abstract

This paper is divided into two logical parts. In the first part of this paper, we prove the following 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.Let V be a vector space of dimension n over a finite field of size q. Let K = {k1,…,kr}, L = {μ1,…,μs} be two disjoint subsets of {0,1,…,b-1} with k1<….< kr. Let F = {V1,V2,…,Vm} be a family of subspaces of V such that (a) for every i ∈ [m], dim(Vi) mod b = kt, for some kt ∈ K, and (b) for every distinct i,j ∈ [m], dim(Vi ∩ Vj)mod b = μt, for some μt ∈ L. Moreover, it is given that neither of the following two conditions hold:(i) q + 1 is a power of 2, and b = 2 (ii) q = 2, b = 6. Then, (formula presented) otherwise, where (formula presented) In the second part of this paper, we prove q-analogues of results on a recent notion called fractional L-intersecting family of sets for families of subspaces of a given vector space over a finite field of size q. 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. © The authors.

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IITH Creators:
IITH CreatorsORCiD
Mathew, R.https://orcid.org/0000-0003-4536-1136
Item Type: Article
Additional Information: ∗This author was supported by a grant from the Science and Engineering Research Board, Department of Science and Technology, Govt. of India (project number: MTR/2019/000550).
Uncontrolled Keywords: generalized modular Ray-Chaudhuri-Wilson Theorem,fractional L-intersecting family ,
Subjects: Computer science
Electrical Engineering
Divisions: Department of Civil Engineering
Department of Electrical Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 19 Jul 2022 09:46
Last Modified: 19 Jul 2022 09:48
URI: http://raiith.iith.ac.in/id/eprint/9789
Publisher URL: http://doi.org/10.37236/10358
OA policy: https://v2.sherpa.ac.uk/id/publication/30650
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