The Rank-Generating Functions of Upho Posets
Abstract
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.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.01916
- arXiv:
- arXiv:2011.01916
- Bibcode:
- 2020arXiv201101916G
- Keywords:
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- Mathematics - Combinatorics