用二次Gröbner基证明多角理想的素性
Primality of polyomino ideals by quadratic Gröbner basis
摘要：
在这项工作中，我们提供了一个充要条件的polyomino理想有一组内2-子式作为度逆字典Gröbner基，由于组合性质的polyomino本身。此外，我们还证明了当后者成立时，理想与关联于四角多面体的格理想重合，即理想是素的。作为应用，我们描述了两个新的素多项式无限族。
英文摘要：
In this work, we provide a necessary and sufficient condition on a polyomino ideal for having the set of inner 2-minors as degree reverse lexicographic Gröbner basis, due to combinatorial properties of the polyomino itself. Moreover, we prove that when the latter holds the ideal coincides with the lattice ideal associated to the polyomino, that is the ideal is prime. As an application, we describe two new infinite families of prime polyominoes.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
