Pregled bibliografske jedinice broj: 1094913
Additive triples of bijections, or the toroidal semiqueens problem
Additive triples of bijections, or the toroidal semiqueens problem // Journal of the european mathematical society, 21 (2019), 2; 441-463 doi:10.4171/jems/841 (međunarodna recenzija, članak, znanstveni)
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Naslov
Additive triples of bijections, or the toroidal
semiqueens problem
Autori
Eberhard, Sean ; Manners, Freddie ; Mrazović, Rudi
Izvornik
Journal of the european mathematical society (1435-9855) 21
(2019), 2;
441-463
Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni
Ključne riječi
Hardy–Littlewood circle method, transversals in Latin squares, permutations
Sažetak
We prove an asymptotic for the number of additive triples of bijections {; ; 1, …, n}; ; →Z/nZ, that is, the number of pairs of bijections π1, π2:{; ; 1, …, n}; ; →Z/nZ such that the pointwise sum π1+π2 is also a bijection. This problem is equivalent to counting the number of orthomorphisms or complete mappings of Z/nZ, to counting the number of arrangements of n mutually nonattacking semiqueens on an n×n toroidal chessboard, and to counting the number of transversals in a cyclic Latin square. The method of proof is a version of the Hardy– Littlewood circle method from analytic number theory, adapted to the group (Z/nZ)^n.
Izvorni jezik
Engleski
Znanstvena područja
Matematika
POVEZANOST RADA
Ustanove:
Prirodoslovno-matematički fakultet, Matematički odjel, Zagreb,
Prirodoslovno-matematički fakultet, Zagreb
Profili:
Rudi Mrazović
(autor)
Citiraj ovu publikaciju:
Časopis indeksira:
- Current Contents Connect (CCC)
- Web of Science Core Collection (WoSCC)
- Science Citation Index Expanded (SCI-EXP)
- SCI-EXP, SSCI i/ili A&HCI
- Scopus
