Repeatedly applying the Combinatorial Nullstellensatz for Zero-sum Grids to Martin Gardner’s minimum no-3-in-a-line problem

IF 1 3区 数学 Q1 MATHEMATICS
Seunghwan Oh , John R. Schmitt , Xianzhi Wang
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引用次数: 0

Abstract

A 1976 question of Martin Gardner asks for the minimum size of a placement of queens on an n×n chessboard that is maximal with respect to the property of ‘no-3-in-a-line’. The work of Cooper, Pikhurko, Schmitt and Warrington showed that this number is at least n in the cases that n3(mod4), and at least n1 in the case that n3(mod4). When n>1 is odd, Gardner conjectured the lower bound to be n+1. We prove this conjecture in the case that n1(mod4). The proof relies heavily on a recent advancement to the Combinatorial Nullstellensatz for zero-sum grids due to Bogdan Nica.
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来源期刊
CiteScore
2.10
自引率
10.00%
发文量
124
审稿时长
4-8 weeks
期刊介绍: The European Journal of Combinatorics is a high standard, international, bimonthly journal of pure mathematics, specializing in theories arising from combinatorial problems. The journal is primarily open to papers dealing with mathematical structures within combinatorics and/or establishing direct links between combinatorics and other branches of mathematics and the theories of computing. The journal includes full-length research papers on important topics.
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