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The existence of large set of symmetric partitioned incomplete latin squares
Author(s) -
Shen Cong,
Cao Haitao,
Ji Lijun
Publication year - 2020
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/jcd.21703
Subject(s) - mathematics , combinatorics , generalization , latin square , set (abstract data type) , type (biology) , discrete mathematics , computer science , mathematical analysis , rumen , chemistry , food science , fermentation , programming language , ecology , biology
In this paper, we investigate the existence of large sets of symmetric partitioned incomplete latin squares of type g u (LSSPILSs) which can be viewed as a generalization of the well‐known golf designs. Constructions for LSSPILSs are presented from some other large sets, such as golf designs, large sets of group divisible designs, and large sets of Room frames. We prove that there exists an LSSPILS( g u ) if and only if u ≥ 3, g ( u − 1) ≡ 0 (mod 2), and ( g , u ) ≠ (1, 5).