Naslov
An asymptotic for the Hall–Paige conjecture

Autori
Eberhard, Sean ; Manners, Freddie ; Mrazović, Rudi

Izvornik
Advances in mathematics (0001-8708) 404 (2022), Part A; 108423, 73

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Hall–Paige conjecture ; Transversals ; Latin squares

Sažetak
Hall and Paige conjectured in 1955 that a finite group G has a complete mapping if and only if its Sylow 2-subgroups are trivial or noncyclic. This conjecture was proved in 2009 by Wilcox, Evans, and Bray using the classification of finite simple groups and extensive computer algebra. Using a completely different approach motivated by the circle method from analytic number theory, we prove that the number of complete mappings of any group G of order n satisfying the Hall–Paige condition is (e^{; ; -1/2}; ; + o(1)) |G^\ab| n!^2/n^n.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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