Back to Search
Start Over
Transversals in quasirandom latin squares.
- Source :
- Proceedings of the London Mathematical Society; Jul2023, Vol. 127 Issue 1, p84-115, 32p
- Publication Year :
- 2023
-
Abstract
- A transversal in an n×n$n \times n$ latin square is a collection of n$n$ entries not repeating any row, column, or symbol. Kwan showed that almost every n×n$n \times n$ latin square has (1+o(1))n/e2n$\bigl ((1 + o(1)) n / e^2\bigr)^n$ transversals as n→∞$n \rightarrow \infty$. Using a loose variant of the circle method we sharpen this to (e−1/2+o(1))n!2/nn$(e^{-1/2} + o(1)) n!^2 / n^n$. Our method works for all latin squares satisfying a certain quasirandomness condition, which includes both random latin squares with high probability as well as multiplication tables of quasirandom groups. [ABSTRACT FROM AUTHOR]
- Subjects :
- MAGIC squares
TRANSVERSAL lines
Subjects
Details
- Language :
- English
- ISSN :
- 00246115
- Volume :
- 127
- Issue :
- 1
- Database :
- Complementary Index
- Journal :
- Proceedings of the London Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 164701276
- Full Text :
- https://doi.org/10.1112/plms.12538