On Computing the Number of Latin Rectangles

Rebecca J. Stones, Sheng Lin, Xiaoguang Liu, Gang Wang

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)

Abstract

Doyle (circa 1980) found a formula for the number of (Formula presented.) Latin rectangles (Formula presented.). This formula remained dormant until it was recently used for counting (Formula presented.) Latin rectangles, where (Formula presented.). We give a formal proof of Doyle’s formula for arbitrary k. We also improve a previous implementation of this formula, which we use to find (Formula presented.) when (Formula presented.) and (Formula presented.) , when (Formula presented.) and (Formula presented.) and when (Formula presented.) and (Formula presented.). Motivated by computational data for (Formula presented.) , some research problems and conjectures about the divisors of (Formula presented.) are presented.

Original languageEnglish
Pages (from-to)1187-1202
Number of pages16
JournalGraphs and Combinatorics
Volume32
Issue number3
DOIs
Publication statusPublished - 1 May 2016

Keywords

  • Latin rectangle
  • Latin square

Cite this

Stones, R. J., Lin, S., Liu, X., & Wang, G. (2016). On Computing the Number of Latin Rectangles. Graphs and Combinatorics, 32(3), 1187-1202. https://doi.org/10.1007/s00373-015-1643-1