膨胀闭路多联骨牌的素性
Primality of dilated closed path polyominoes
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中文总结 AI 辅助
本文定义多联骨牌的张量积及其特例膨胀，构造膨胀闭路类，证明Zig-Zag游走猜想，完全刻画了相关多联骨牌理想的素性。
中文摘要 AI 辅助
本文定义了一种新的多联骨牌乘积，称为多联骨牌的张量积。利用该乘积的一个特例（我们称之为膨胀），我们构造了一类新的多联骨牌，称为膨胀闭路。该类是Cisto和Navarra的闭路类（arXiv:2006.13935）的“厚”推广。我们证明了这类新多联骨牌的Zig-Zag游走猜想，从而完全刻画了其相关多联骨牌理想的素性。
英文摘要
In this paper we define a novel product on polyominoes called the tensor product of polyominoes. Using a special case of this product which we name a dilation, we construct a new class of polyominoes called the dilated closed paths. This class is a ''thick'' generalization of Cisto and Navarra's class of closed paths (arXiv:2006.13935). We prove the Zig-Zag Walk Conjecture for this new class thereby fully characterizing primality for its associated polyomino ideals.
