论文标题
upho posets的等级生成功能
The Rank-Generating Functions of Upho Posets
论文作者
论文摘要
上部有限类型（Upho）Posets是一类大型部分有序的集合，其属性具有每个顶点的主秩序过滤器对整个POSET都是同构的。众所周知的例子包括K阵列树，网格图和船尾poset。一般来说，关于Upho Posets的知之甚少。在本文中，我们用Schur阳性Ehrenborg的甲酸对称函数构建了tho posets，其级别生成功能具有有理极和零。我们还对所有平面upho posets的秩函数进行了分类。最后，我们证明了具有无法兼容的秩函数的尖端poset的存在。
Upper homogeneous finite type (upho) posets are a large class of partially ordered sets with the property that the principal order filter at every vertex is isomorphic to the whole poset. Well-known examples include k-array trees, the grid graphs, and the Stern poset. Very little is known about upho posets in general. In this paper, we construct upho posets with Schur-positive Ehrenborg quasisymmetric functions, whose rank-generating functions have rational poles and zeros. We also categorize the rank-generating functions of all planar upho posets. Finally, we prove the existence of an upho poset with uncomputable rank-generating function.
