Some enumerative properties of a class of Fibonacci-like cubes

2019/05/02 by Xuxu Zhao, Xu Wang, Zhao, Xuxu +3
Computer Science · Mathematics · #05C70 #06A07 #06D05 #11B39 #Advanced Algebra and Logic #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics #Combinatorics (math.CO) #Cube (algebra) #Discrete mathematics #Distributive lattice #Distributive property #FOS: Mathematics #Fibonacci number #Generating function #Hasse diagram #Lattice (music) #Mathematics #Partially ordered set #Physics #Pure mathematics #Sequence (biology) #math.CO #msc:05C70 #msc:06A07 #msc:06D05 #msc:11B39

paper · pdf · doi:10.48550/arxiv.1905.00573

13 pages, 5 figures

arxiv created 2019/05/02 · openalex publication_date 2019/05/02 · arxiv updated 2019/05/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

A filter lattice is a distributive lattice formed by all filters of a poset in the anti-inclusion order. We study the combinatorial properties of the Hasse diagrams of filter lattices of certain posets, so called Fibonacci-like cubes, in this paper. Several enumerative polynomials, e.g. rank generating function, cube polynomials and degree sequence polynomials are obtained. Some of these results relate to Fibonacci sequence and Padovan sequence.

Citations

• The on-line encyclopedia of integer sequences
• Convex expansion for finite distributive lattices with applications

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