
TL;DR
This paper studies the enumeration and structure of various classes of graded posets, providing new theorems and generalizations, and connecting classical results with modern combinatorial questions.
Contribution
It introduces new enumerative and structural results for classes of graded posets, generalizes existing theorems, and addresses open questions in the field.
Findings
Enumerative formulas for graded posets
Structural theorems for (2+2)- and (3+1)-avoiding posets
Connections between labeled and unlabeled poset enumeration
Abstract
We explore the enumeration of some natural classes of graded posets, including all graded posets, (2+2)- and (3+1)-avoiding graded posets, (2+2)-avoiding graded posets, and (3+1)-avoiding graded posets. We obtain enumerative and structural theorems for all of them. Along the way, we discuss a situation when we can switch between enumeration of labeled and unlabeled objects with ease, generalize a result of Postnikov and Stanley from the theory of hyperplane arrangements, answer a question posed by Stanley, and see an old result of Klarner in a new light.
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
TopicsAdvanced Combinatorial Mathematics · Algebraic structures and combinatorial models · Commutative Algebra and Its Applications
