Séminaire Lotharingien de Combinatoire, 91B.104 (2024), 12 pp.
Ziyao Fu, Yulin Peng and Yuchong Zhang
The Monoid epresentation of Upho Posets and Total Positivity
Abstract.
In this paper, we establish a bijection between finitary colored upho posets and left-cancellative invertible-free monoids. This bijection maps $\N$-graded colored upho posets to left-cancellative homogeneous monoids. We use this bijection and the new concept of semi-upho posets to prove that every totally positive power series is the rank-generating function of some upho poset, resolving a conjecture of Gao et al.
Received: November 15, 2023.
Accepted: February 15, 2024.
Final version: April 1, 2024.
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