The Generalized Interval Polynomial of a Poset

2025/11/18 by George, Ian, Yeats, Karen
Physics and Astronomy · Mathematics · #Noncommutative and Quantum Gravity Theories #Mathematical and Theoretical Analysis #Advanced Mathematical Theories and Applications

paper · doi:10.48550/arxiv.2511.14924

Abstract

For any finite poset we define a generating polynomial counting upsets, downsets, and their intersection. We investigate the behaviour of this polynomial with respect to poset operations, show that it distinguishes series-parallel posets, and comment on connections to the causal set approach to quantum gravity.

Citations

• Enumeration in the lattice of q-decreasing words
• Intervals in a family of Fibonacci lattices
• About maximal antichains in a product of two chains:A catch-all note
• On the generating function for intervals in Young's lattice
• Antichain generating polynomials of posets

Related

• Exponential functions of finite posets and the number of extensions with a fixed set of minimal points
• Antichain generating polynomials of posets
• Linear Intervals in the Tamari and the Dyck Lattices and in the alt-Tamari Posets
• The poset of posets
• A generalization of Chebyshev polynomials and non rooted posets