Modular and fractional Lintersecting families of vector spaces
Mathew, R. and Kumar Mishra, Tapas and Ray, Ritabrata and Srivastava, Shashank (2022) Modular and fractional Lintersecting families of vector spaces. The Electronic Journal of Combinatorics, 29 (1). pp. 120. ISSN 10778926
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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 qanalogue of a generalized modular RayChaudhuriWilson 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,…,b1} 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 qanalogues of results on a recent notion called fractional Lintersecting 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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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 RayChaudhuriWilson Theorem,fractional Lintersecting 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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