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The existence of r ‐golf designs
Author(s) -
Li Xiangqian,
Chang Yanxun,
Zhou Junling
Publication year - 2021
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.21766
Subject(s) - mathematics , idempotence , integer (computer science) , combinatorics , order (exchange) , latin square , set (abstract data type) , discrete mathematics , computer science , rumen , chemistry , food science , finance , economics , programming language , fermentation
An r ‐golf design of order v , briefly by r ‐G( v ), is a large set of idempotent Latin squares of order v (ILS ( v ) s) which contains r symmetric ILS ( v ) s andv − r − 2 2 transposed pairs of ILS ( v ) s. In this paper, we mainly consider the existence problem of r ‐G( v )s. We present several recursive constructions and also display some direct constructions. As an application, several infinite classes of r ‐G( v )s are determined, including the existence of 0‐G( v )s for more than half of admissible parameters and the existence of r ‐G( v )s where v ≡ 11( mod 24 ) and r is any admissible integer ( r odd and 1 ≤ r ≤ v − 2 ).