arXiv
Open Access
2022
Row-Hamiltonian Latin squares and Falconer varieties
Jack Allsop
Ian M. Wanless
Abstrak
A \emph{Latin square} is a matrix of symbols such that each symbol occurs exactly once in each row and column. A Latin square $L$ is \emph{row-Hamiltonian} if the permutation induced by each pair of distinct rows of $L$ is a full cycle permutation. Row-Hamiltonian Latin squares are equivalent to perfect $1$-factorisations of complete bipartite graphs. For the first time, we exhibit a family of Latin squares that are row-Hamiltonian and also achieve precisely one of the related properties of being column-Hamiltonian or symbol-Hamiltonian. This family allows us to construct non-trivial, anti-associative, isotopically $L$-closed loop varieties, solving an open problem posed by Falconer in 1970.
Topik & Kata Kunci
Penulis (2)
J
Jack Allsop
I
Ian M. Wanless
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2022
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- en
- Sumber Database
- arXiv
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- Open Access ✓