Fractional Cross Intersecting Families

Mathew, Rogers and Ray, Ritabrata and Srivastava, Shashank (2021) Fractional Cross Intersecting Families. Graphs and Combinatorics, 37 (2). pp. 471-484. ISSN 0911-0119

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Abstract

Let A= { A1, … , Ap} and B= { B1, … , Bq} be two families of subsets of [n] such that for every i∈ [p] and j∈ [q] , |Ai∩Bj|=cd|Bj|, where cd∈[0,1] is an irreducible fraction. We call such families cd-cross intersecting families. In this paper, we find a tight upper bound for the product | A| | B| and characterize the cases when this bound is achieved for cd=12. Also, we find a tight upper bound on | A| | B| when B is k-uniform and characterize, for all cd, the cases when this bound is achieved. © 2020, Springer Japan KK, part of Springer Nature.

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IITH Creators:

IITH Creators	ORCiD
Mathew, Rogers	https://orcid.org/0000-0003-4536-1136

Item Type:

Article

Additional Information:

Rogers Mathew 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:

Cross-bisecting family; Cross-intersecting family; Fractional intersecting family; Linear code

Subjects:

Computer science

Divisions:

Department of Computer Science & Engineering

Depositing User:

. LibTrainee 2021

Date Deposited:

24 Aug 2022 09:08

Last Modified:

24 Aug 2022 09:08