The Spectrum of Premature Partial Latin Squares

Ljiljana Brankovic; Mirka Miller

The Spectrum of Premature Partial Latin Squares

Ljiljana Brankovic
, Mirka Miller

Computer Science

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

A premature partiallatin square of order n, denoted PPLS(n) is a partial latin square which cannot be completed but removing any of its entries destroys this property, that is, then there is at least one completion. The spectrum of PPLSs is the set P(n) = {t | there exists a PPLS(n) with exactly t nonempty cells}.

In this paper we give an overview of known results and present an improvement of the upper bound on the maximum value of the spectrum for a restricted class of PPLSs. The paper concludes with several open problems in the area.

Original language	English
Title of host publication	Proceedings of the Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99)
Editors	Rajeev Raman, Jamie Simpson
Place of Publication	Perth, Australia
Publisher	Curtin University Press
Pages	168-175
Volume	3
ISBN (Print)	186342802X
Publication status	Published - 31 Jul 1999
Event	AWOCA 1999: Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99) - Curtin University of Technology, Perth, Australia Duration: 25 Jul 1999 → 27 Jul 1999

Conference

Conference	AWOCA 1999: Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99)
City	Perth, Australia
Period	25/07/99 → 27/07/99

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@inproceedings{3a44738976324ae289f74f8df3f72927,

title = "The Spectrum of Premature Partial Latin Squares",

abstract = "A premature partiallatin square of order n, denoted PPLS(n) is a partial latin square which cannot be completed but removing any of its entries destroys this property, that is, then there is at least one completion. The spectrum of PPLSs is the set P(n) = \{t | there exists a PPLS(n) with exactly t nonempty cells\}. In this paper we give an overview of known results and present an improvement of the upper bound on the maximum value of the spectrum for a restricted class of PPLSs. The paper concludes with several open problems in the area. ",

author = "Ljiljana Brankovic and Mirka Miller",

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booktitle = "Proceedings of the Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA{\textquoteright}99)",

publisher = "Curtin University Press",

note = "AWOCA 1999: Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA{\textquoteright}99) ; Conference date: 25-07-1999 Through 27-07-1999",

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Brankovic, L & Miller, M 1999, The Spectrum of Premature Partial Latin Squares. in R Raman & J Simpson (eds), Proceedings of the Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99). vol. 3, Curtin University Press, Perth, Australia, pp. 168-175, AWOCA 1999: Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99), Perth, Australia, 25/07/99. <https://hdl.handle.net/1959.11/63412>

The Spectrum of Premature Partial Latin Squares. / Brankovic, Ljiljana; Miller, Mirka.
Proceedings of the Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99). ed. / Rajeev Raman; Jamie Simpson. Vol. 3 Perth, Australia: Curtin University Press, 1999. p. 168-175.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

TY - GEN

T1 - The Spectrum of Premature Partial Latin Squares

AU - Brankovic, Ljiljana

AU - Miller, Mirka

PY - 1999/7/31

Y1 - 1999/7/31

N2 - A premature partiallatin square of order n, denoted PPLS(n) is a partial latin square which cannot be completed but removing any of its entries destroys this property, that is, then there is at least one completion. The spectrum of PPLSs is the set P(n) = {t | there exists a PPLS(n) with exactly t nonempty cells}. In this paper we give an overview of known results and present an improvement of the upper bound on the maximum value of the spectrum for a restricted class of PPLSs. The paper concludes with several open problems in the area.

AB - A premature partiallatin square of order n, denoted PPLS(n) is a partial latin square which cannot be completed but removing any of its entries destroys this property, that is, then there is at least one completion. The spectrum of PPLSs is the set P(n) = {t | there exists a PPLS(n) with exactly t nonempty cells}. In this paper we give an overview of known results and present an improvement of the upper bound on the maximum value of the spectrum for a restricted class of PPLSs. The paper concludes with several open problems in the area.

M3 - Conference contribution

SN - 186342802X

VL - 3

SP - 168

EP - 175

BT - Proceedings of the Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99)

A2 - Raman, Rajeev

A2 - Simpson, Jamie

PB - Curtin University Press

CY - Perth, Australia

T2 - AWOCA 1999: Tenth Australasian Workshop on Combinatorial Algorithms (AWOCA’99)

Y2 - 25 July 1999 through 27 July 1999

ER -

The Spectrum of Premature Partial Latin Squares

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