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A Generating Polynomial for Convex Subsets of Posets
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 and show that it distinguishes certain posets constructed with the operations of ordinal sum and disjoint union, including Series-Parallel posets as a special case. Lastly, we comment on connections to the causal set approach to quantum gravity.
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BibTeX
@misc{george2026generating,
title = {{A Generating Polynomial for Convex Subsets of Posets}},
author = {Ian George and Rowan Yeats},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.23399},
eprint = {2610.23399},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.23399},
}
RIS
TY - UNPB
TI - A Generating Polynomial for Convex Subsets of Posets
AU - Ian George
AU - Rowan Yeats
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.23399
UR - https://arxiv.org/abs/2610.23399
AB - 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 and show that it distinguishes certain posets constructed with the operations of ordinal sum and disjoint union, including Series-Parallel posets as a special case. Lastly, we comment on connections to the causal set approach to quantum gravity.
ER -