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arXiv · 1810.07329

Structure and enumeration results of matchable Lucas cubes

Xu Wang·Xuxu Zhao·Haiyuan Yao
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Abstract

A lucasene is a hexagon chain that is similar to a fibonaccene, an $L$-fence is a poset the Hasse diagram of which is isomorphic to the directed inner dual graph of the corresponding lucasene. A new class of cubes, which named after matchable Lucas cubes according to the number of its vertices (or elements), are a series of directed or undirected Hasse diagrams of filter lattices of $L$-fences. The basic properties and several classes of polynomials, e.g.\ rank generating functions, cube polynomials and degree sequence polynomials, of matchable Lucas cubes are obtained. Some special conclusions on binomial coefficients and Lucas triangle are given.

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Xu Wang, Xuxu Zhao, Haiyuan Yao. 2018-10-17. Structure and enumeration results of matchable Lucas cubes. https://arxiv.org/abs/1810.07329

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