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Title: On cross Parsons numbers
Authors: Ku, Cheng Yeaw
Wong, Kok Bin
Keywords: Science::Mathematics
Issue Date: 2019
Source: Ku, C. Y. & Wong, K. B. (2019). On cross Parsons numbers. Graphs and Combinatorics, 35(1), 287-301.
Journal: Graphs and Combinatorics
Abstract: Let Fq be the field of size q and SL(n, q) be the special linear group of order n over the field Fq. Assume that n is an even integer. Let Ai⊆SL(n,q) for i=1,2,…,k and |A1|=|A2|=⋯=|Ak|=l. The set {A1,A2,…,Ak} is called a k-cross (n, q)-Parsons set of size l, if for any pair of (i, j) with i≠j, A−B∈SL(n,q) for all A∈Ai and B∈Aj. Let m(k, n, q) be the largest integer l for which there is a k-cross (n, q)-Parsons set of size l. The integer m(k, n, q) will be called the k-cross (n, q)-Parsons numbers. In this paper, we will show that m(3,2,q)≤q. Furthermore, m(3,2,q)=q if and only if q=4r for some positive integer r. We will also show that if n is a multiple of q−1, then m(q−1,n,q)≥q12n(n−1).
ISSN: 0911-0119
DOI: 10.1007/s00373-018-1993-6
Rights: © 2018 Springer Japan KK, part of Springer Nature. All rights reserved.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

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