Year: 2025
Type: article
Abstract: ABSTRACT A partial Latin rectangle is if the number of nonempty entries in each row and column is at most and each symbol is used at most times. We prove that the probability a uniformly random Latin rectangle, where , contains a ‐sparse partial Latin rectangle with nonempty entries is for sufficiently large and sufficiently small . Using this result, we prove that a uniformly random order‐ Latin square asymptotically almost surely has no Latin subsquare of order greater than for an absolute constant .
Source: Journal of Combinatorial Designs
DOI: 10.1002/jcd.70004
Authors: Alexander Divoux, Tom Kelly, Camille Kennedy, Jasdeep Sidhu
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,350
Awards: RTG: Research Training in Geometry and Topology, Randomness in High-Dimensional Combinatorics: Colorings, Robustness, and Statistics, REU Site: Georgia Institute of Technology Mathematics Research Experiences for Undergraduates, REU Site: Georgia Institute of Technology Mathematics REU Program
OpenAlex ID: W4417485248