All group‐based latin squares possess near transversals | Zendy

Goddyn Luis | Zendy; Halasz Kevin | Zendy

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All group‐based latin squares possess near transversals

Author(s) -

Goddyn Luis,

Halasz Kevin

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.21701

Subject(s) - latin square , transversal (combinatorics) , mathematics , conjecture , combinatorics , square (algebra) , class (philosophy) , order (exchange) , group (periodic table) , column (typography) , symbol (formal) , discrete mathematics , connection (principal bundle) , geometry , computer science , mathematical analysis , physics , artificial intelligence , finance , quantum mechanics , economics , programming language , rumen , chemistry , food science , fermentation

In a latin square of order n , a near transversal is a collection of n −1 cells which intersects each row, column, and symbol class at most once. A longstanding conjecture of Brualdi, Ryser, and Stein asserts that every latin square possesses a near transversal. We show that this conjecture is true for every latin square that is main class equivalent to the Cayley table of a finite group.

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