Stern偏序集的flag f和flag h向量的性质研究
The flag f and flag h Vectors of the Stern’s Poset
DOI: 10.12677/AAM.2021.108273, PDF,   
作者: 林佳倩：辽宁师范大学数学学院，辽宁 大连
关键词: Stern偏序集；flag f向量；flag h向量；Stern’s Poset； flag f Vector； flag h Vector
摘要: Stern偏序集是组合数学中一类非常重要且有趣的偏序集，在组合计数中起到重要的统一作用。本篇论文从计数序理想角度出发，研究了Stern偏序集的flag f和flag h向量，并给出了具体表达公式。
Abstract: The Stern’s poset is one kind of partially ordered set with great importance and interest in Combinatorics, which plays a unifying role in combinatorial counting. In this paper, we study the flag f and flag h vectors of the Stern’s poset from the viewpoint of counting order ideal, and then give the specific expression formulas.
文章引用：林佳倩. Stern偏序集的flag f和flag h向量的性质研究[J]. 应用数学进展, 2021, 10(8): 2633-2638. https://doi.org/10.12677/AAM.2021.108273

参考文献

[1] Rotr, C. (1964) On the Foundations of Combinatorial Theory I, Theory of Mobiousfunctions. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 2, 340-368. [Google Scholar] [CrossRef] 
[2] Stanley, R. (1997) Enumerative Combinatorics Vol. 1. Cambridge University Press, Cambridge. [Google Scholar] [CrossRef] 
[3] Stanley, R. (2020) Some Linear Recurrences Motivated by Stern’s Diatomic Array. The American Mathematical Monthly, 127, 99-111. [Google Scholar] [CrossRef] 
[4] Stanley, R. (2012) Enumerative Combinatorics. 2nd Edition, Vol. 1. Cambridge University Press, Cambridge.
[5] Nyman, K. and Swartz, E. (2004) Inequalities for the h-Vectors and Flag h-Vectors of Geometric Lattices. Discrete & Computational Geometry, 32, 533-548. [Google Scholar] [CrossRef] 
[6] Schweig, J. (2010) Convex-Ear Decompositions and the Flag H-Vector. Electronic Journal of Combinatorics, 18, 4. [Google Scholar] [CrossRef] 
[7] Mu, L. (2020) Some Combinatorial Properties of Hexagonal Poset. Contributions to Discrete Mathematics, 15, 175-182.

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