具有近似凸列的多项式：一个无向模型
Polyominoes with nearly convex columns: An undirected model
摘要：
列凸多角形是在20世纪50年代由一位致力于“格子气体”研究的数学物理学家Temperley提出的。到目前为止，柱凸多项式是一个流行的和很好理解的模型。存在几种列凸多角形的推广;一个例子是称为多向动物的模型。本文引入了一个新的列凸多项式超集序列。我们的模型（我们称之为m级列次凸多项式）是以一种简单的方式定义的。我们专注于当细胞是六边形的情况下，我们计算的面积生成函数的水平一和两个。这两种母函数都是复杂的q-级数，而柱凸多项式的面积母函数是一个有理函数。第一级和第二级列次凸多项式的增长常数分别为4.319139和4.509480。作为比较，柱凸多角形动物、多向动物和全多角形动物的生长常数分别为3.863131、4.587894和5.183148。
英文摘要：
Column-convex polyominoes were introduced in 1950's by Temperley, a mathematical physicist working on "lattice gases". By now, column-convex polyominoes are a popular and well-understood model. There exist several generalizations of column-convex polyominoes; an example is a model called multi-directed animals. In this paper, we introduce a new sequence of supersets of column-convex polyominoes. Our model (we call it level m column-subconvex polyominoes) is defined in a simple way. We focus on the case when cells are hexagons and we compute the area generating functions for the levels one and two. Both of those generating functions are complicated q-series, whereas the area generating function of column-convex polyominoes is a rational function. The growth constants of level one and level two column-subconvex polyominoes are 4.319139 and 4.509480, respectively. For comparison, the growth constants of column-convex polyominoes, multi-directed animals and all polyominoes are 3.863131, 4.587894 and 5.183148, respectively.
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。
