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Cross t-Intersecting Integer Sequences from Weighted Erdős–Ko–Rado

Published online by Cambridge University Press:  09 May 2013

NORIHIDE TOKUSHIGE
NORIHIDE TOKUSHIGE*
Affiliation:
College of Education, Ryukyu University, Nishihara, Okinawa 903-0213, Japan (e-mail: hide@edu.u-ryukyu.ac.jp)
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Abstract

Let m,n and t be positive integers. Consider [m]n as the set of sequences of length n on an m-letter alphabet. We say that two subsets A⊂[m]n and B⊂[m]n cross t-intersect if any two sequences a∈A and b∈B match in at least t positions. In this case it is shown that if $m > (1-\frac 1{\sqrt[t]2})^{-1}$ then |A||B|≤(mn−t)2. We derive this result from a weighted version of the Erdős–Ko–Rado theorem concerning cross t-intersecting families of subsets, and we also include the corresponding stability statement. One of our main tools is the eigenvalue method for intersection matrices due to Friedgut [10].

Keywords

Primary 05D05Secondary 05C50
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 22 , Issue 4 , July 2013 , pp. 622 - 637
Copyright
Copyright © Cambridge University Press 2013 

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