具有近似凸列的多项式：一个具有半定向块的模型
Polyominoes with nearly convex columns: A model with semidirected blocks
摘要：
在今天的大多数精确求解的多项式类中，要么所有成员都是凸的（在某种程度上），要么所有成员都是有向的，或者两者兼而有之。如果类既不是凸的也不是有向的，则精确解通常是难以捉摸的。本文主要研究具有六角胞腔的多角形问题。具体地说，我们处理的polyominoes的列可以有一个或两个连接的组件。这些多角形（不像已被充分研究的列凸多角形）不能被任何现有的方法精确枚举。因此，适当地引入额外的限制，从而获得可解的子类。在我们最近发表在同一杂志上的论文中，刚刚提到的限制是半定向性和列内间隙大小的上界。在本文中，半有向性的要求是宽松的。结果是，现在精确求解的子类更大，并且具有更大的增长常数。这些新的polyomino族也有优点，是不变的反射下的垂直轴。
英文摘要：
In most of today's exactly solved classes of polyominoes, either all members are convex (in some way), or all members are directed, or both. If the class is neither convex nor directed, the exact solution uses to be elusive. This paper is focused on polyominoes with hexagonal cells. Concretely, we deal with polyominoes whose columns can have either one or two connected components. Those polyominoes (unlike the well-explored column-convex polyominoes) cannot be exactly enumerated by any of the now existing methods. It is therefore appropriate to introduce additional restrictions, thus obtaining solvable subclasses. In our recent paper, published in this same journal, the restrictions just mentioned were semidirectedness and an upper bound on the size of the gap within a column. In this paper, the semidirectedness requirement is made looser. The result is that now the exactly solved subclasses are larger and have greater growth constants. These new polyomino families also have the advantage of being invariant under the reflection about the vertical axis.
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。
