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September 2020 Primality of multiply connected polyominoes
Carla Mascia, Giancarlo Rinaldo, Francesco Romeo
Illinois J. Math. 64(3): 291-304 (September 2020). DOI: 10.1215/00192082-8591560

Abstract

It is known that the polyomino ideal of simple polyominoes is prime. In this paper, we focus on multiply connected polyominoes, namely polyominoes with holes, and observe that the nonexistence of a certain sequence of inner intervals of the polyomino, called zig-zag walk, gives a necessary condition for the primality of the polyomino ideal. Moreover, by computational approach, we prove that for all polyominoes with rank less than or equal to 14 , the above condition is also sufficient. Lastly, we present an infinite new class of prime polyomino ideals.

Citation

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Carla Mascia. Giancarlo Rinaldo. Francesco Romeo. "Primality of multiply connected polyominoes." Illinois J. Math. 64 (3) 291 - 304, September 2020. https://doi.org/10.1215/00192082-8591560

Information

Received: 26 July 2019; Revised: 14 March 2020; Published: September 2020
First available in Project Euclid: 1 July 2020

zbMATH: 07235504
MathSciNet: MR4132592
Digital Object Identifier: 10.1215/00192082-8591560

Subjects:
Primary: 05E40
Secondary: 13A02

Rights: Copyright © 2020 University of Illinois at Urbana-Champaign

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Vol.64 • No. 3 • September 2020
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