一类斐波那契相似立方体及其计数性质  

A Class of Fibonacci Similar Cubes and Their Counting Properties

作　　者：周玉玉 陈芳娣 赵姁姁 

机构地区：[1]西北师范大学,数学与统计学院,甘肃 兰州 [2]甘肃省陕西师范大学平凉实验中学,甘肃 平凉

出　　处：《理论数学》2023年第12期3676-3689,共14页Pure Mathematics

摘　　要：L-si-Fibonaccene是一个基于Fibonaccene简单变形得到的六角系统,在其内对偶图上建立了一种特殊偏序,命名为L-栅栏。根据偏序L-栅栏的所有滤子按照反包含关系形成的滤子格,得到了一类新的匹配型分配格,忽略掉其Hasse图中的方向后就得到一个结构和性质都与斐波那契立方体相似的新立方体,并计算了它的秩生成函数、立方体多项式和极大立方体多项式.本文的研究不但为匹配型分配格增加了一类新成员,而且其导出的立方体还可以作为新的内联网的模型。L-si-Fibonaccene is a hexagonal system based on the simple deformation of Fibonaccene, and a special partial order is established on its dual graph, which is named L-fence. According to the filter lattice formed by all the filters of the partially ordered L-barrier according to the inverse inclusion relation, a new class of matched distributive lattices is obtained. After ignoring the direction in its Hasse diagram, a new cube with similar structure and properties to the Fibonacci cube is obtained, and its rank generating function, cube polynomial and maximal cube polynomial are calculated. The research in this paper not only adds a new class of members to the matching distributive lattice, but also the derived cube can be used as a new model of the intranet.

关 键 词：匹配型分配格 滤子格 计数性质 斐波那契相似立方体 秩生成函数 立方体多项式 

分 类 号：O15[理学—数学]