A Lattice Path Interpretation of the Diamond Product
Norman Bradley Fox
TL;DR
This paper introduces a lattice path interpretation for the diamond product of cd-polynomials, which arises from the face lattice operation on polytopes and their Eulerian posets, providing a combinatorial perspective.
Contribution
It presents a novel lattice path interpretation of the diamond product on cd-polynomials, linking poset operations with combinatorial lattice paths.
Findings
Provides a combinatorial lattice path model for the diamond product
Connects face lattice operations with cd-polynomial algebra
Enhances understanding of Eulerian poset products
Abstract
The diamond product is the poset operation that when applied to the face lattices of two polytopes results in the face lattice of the Cartesian product of the polytopes. Application of the diamond product to two Eulerian posets is a bilinear operation on the cd-indices of the two posets, yielding a product on cd-polynomials. A lattice path interpretation is provided for this product of two cd-monomials.
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 · Advanced Mathematical Identities · Algebraic structures and combinatorial models