一类有向斐波那契相似立方体的度相关计数性质
The Enumerative Properties Related to Degree of a Class of Directed Fibonacci-Like Cubes
DOI: 10.12677/pm.2024.147288, PDF,    国家自然科学基金支持
作者: 陈芳娣, 张诗晗*：西北师范大学数学与统计学院，甘肃 兰州；赵姁姁：陕西师范大学平凉实验中学，甘肃 平凉
关键词: 匹配型分配格；有向斐波那契相似立方体；出度多项式；出入度多项式；Matchable Distributive Lattice； Directed Fibonacci-Like Cube； Out-Degree Polynomial； In-Out Degree Polynomial
摘要: 匹配型分配格将偏序集和平面基本二部图紧密地联系起来。本文根据一类匹配型分配格的Hasse图，得到了一类有向斐波那契相似立方体，并研究了其度序列多项式、出度多项式和出入度多项式。
Abstract: The matchable distributive lattices closely connect the poset with the planar elementary bipartite graphs. In this paper, according to the Hasse diagrams of a class of matchable distributive lattices, a class of directed Fibonacci-like cubes is obtained and their degree sequence polynomials, out-degree polynomials and in-out degree polynomials are studied.
文章引用：陈芳娣, 张诗晗, 赵姁姁. 一类有向斐波那契相似立方体的度相关计数性质[J]. 理论数学, 2024, 14(7): 211-222. https://doi.org/10.12677/pm.2024.147288

参考文献

[1] Hsu, W.J. (1993) Fibonacci Cubes-A New Interconnection Topology. IEEE Transactions on Parallel and Distributed Systems, 4, 3-12. [Google Scholar] [CrossRef] 
[2] Munarini, E., Cippo, C.P. and Zagaglia Salvi, N. (2001) On the Lucas Cubes. The Fibonacci Quarterly, 39, 12-21.
[3] Klavžar, S. and Žigert Pleteršek, P. (2005) Fibonacci Cubes Are the Resonance Graphs of Fibonaccenes. The Fibonacci Quarterly, 43, 269-276.
[4] Klavžar, S. and Mollard, M. (2011) Cube Polynomial of Fibonacci and Lucas Cubes. Acta Applicandae Mathematicae, 117, 93-105. [Google Scholar] [CrossRef] 
[5] Munarini, E. and Zagaglia Salvi, N. (2002) On the Rank Polynomial of the Lattice of Order Ideals of Fences and Crowns. Discrete Mathematics, 259, 163-177. [Google Scholar] [CrossRef] 
[6] Saygı, E. and Eğecioğlu, Ö. (2016) Counting Disjoint Hypercubes in Fibonacci Cubes. Discrete Applied Mathematics, 215, 231-237. [Google Scholar] [CrossRef] 
[7] Saygi, E. and Eğecioğlu, Ö. (2018) q-Counting Hypercubes in Lucas Cubes. Turkish Journal of Mathematics, 42, 190-203. [Google Scholar] [CrossRef] 
[8] Mollard, M. (2012) Maximal Hypercubes in Fibonacci and Lucas Cubes. Discrete Applied Mathematics, 160, 2479-2483. [Google Scholar] [CrossRef] 
[9] Klavžar, S., Mollard, M. and Petkovšek, M. (2011) The Degree Sequence of Fibonacci and Lucas Cubes. Discrete Mathematics, 311, 1310-1322. [Google Scholar] [CrossRef] 
[10] Lam, P.C.B. and Zhang, H. (2003) A Distributive Lattice on the Set of Perfect Matchings of a Plane Bipartite Graph. Order, 20, 13-29.
[11] Zhang, H., Yang, D. and Yao, H. (2014) Decomposition Theorem on Matchable Distributive Lattices. Discrete Applied Mathematics, 166, 239-248. [Google Scholar] [CrossRef] 
[12] Wang, X., Zhao, X. and Yao, H. (2018) Convex Expansion for Finite Distributive Lattices with Applications. arXiv: 1810.06762.
[13] Wang, X., Zhao, X. and Yao, H. (2018) Structure and Enumeration Results of Matchable Lucas Cubes. arXiv: 1810.07329.
[14] 周玉玉, 陈芳娣, 赵姁姁. 一类斐波那契相似立方体及其计数性质[J]. 理论数学, 2023, 13(12): 3676-3689.

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