Generating Posets with Interfaces
Olavi \"Aik\"as, Uli Fahrenberg, Christian Johansen, Krzysztof, Ziemia\'nski

TL;DR
This paper introduces a new class of iposets with full interfaces, enabling enumeration and analysis of isomorphism classes of posets with interfaces, supported by Julia software and a polynomial-time isomorphism invariant.
Contribution
It defines a new class of iposets with full interfaces and demonstrates their sufficiency for enumeration, along with developing software and a polynomial-time isomorphism invariant.
Findings
Successfully generated and counted iposets up to eight points
Developed Julia software for poset exploration
Created a polynomial-time isomorphism invariant
Abstract
We generate and count isomorphism classes of gluing-parallel posets with interfaces (iposets) on up to eight points, and on up to ten points with interfaces removed. In order to do so, we introduce a new class of iposets with full interfaces and show that considering these is sufficient. We also describe the software (written in Julia) that we have used for our exploration and define a new incomplete isomorphism invariant which may be computed in polynomial time yet identifies only very few pairs of non-isomorphic iposets.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
Topicssemigroups and automata theory · Polynomial and algebraic computation · Advanced Combinatorial Mathematics
