论文标题
在Gröbner基地和Cohen-Macaulay属性上
On Gröbner bases and Cohen-Macaulay property of closed path polyominoes
论文作者
论文摘要
在本文中，我们引入了一些封闭路径多元的单一订单，我们证明了附着在封闭路径上的多元理想的发电机集形成了相对于这些单个单体订单的减少的gröbner基础。众所周知，附着在包含L-配置的封闭路径或至少三个步骤（等效地没有锯齿形步行的梯子）的封闭路径上的多元理想是素数。结果，我们获得没有锯齿形步行的闭合路径的坐标环是正常的Cohen-Macaulay域。
In this paper we introduce some monomial orders for the class of closed path polyominoes and we prove that the set of the generators of the polyomino ideal attached to a closed path forms the reduced Gröbner basis with respect to these monomial orders. It is known that the polyomino ideal attached to a closed path containing an L-configuration or a ladder of at least three steps, equivalently having no zig-zag walks, is prime. As a consequence, we obtain that the coordinate ring of a closed path having no zig-zag walks is a normal Cohen-Macaulay domain.
