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

Text
Electronic_Journal_of_Combinatorics.pdf - Published Version
Available under License Creative Commons Attribution.
Download (374kB)

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.

[error in script]

IITH Creators:

IITH Creators	ORCiD
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