On Computing the Number of Latin Rectangles

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

doi:10.1007/s00373-015-1643-1

On Computing the Number of Latin Rectangles

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

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-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 language	English
Pages (from-to)	1187-1202
Number of pages	16
Journal	Graphs and Combinatorics
Volume	32
Issue number	3
DOIs	https://doi.org/10.1007/s00373-015-1643-1
Publication status	Published - 1 May 2016

Keywords

Latin rectangle
Latin square

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10.1007/s00373-015-1643-1Licence: CC BY

106700878-oaFinal published version, 749 KBLicence: CC BY

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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{\textquoteright}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.",

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T1 - On Computing the Number of Latin Rectangles

AU - Stones, Rebecca J.

AU - Lin, Sheng

AU - Liu, Xiaoguang

AU - Wang, Gang

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Latin rectangle

KW - Latin square

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SP - 1187

EP - 1202

JO - Graphs and Combinatorics

JF - Graphs and Combinatorics

IS - 3

ER -

On Computing the Number of Latin Rectangles

Abstract

Keywords

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