避免双3长Vincular模式排列的计数研究
Enumeration of Permutations Avoiding Double Vincular Patterns of Length 3
DOI: 10.12677/PM.2023.1310322, PDF,    科研立项经费支持
作者: 赵 沨：河北师范大学数学科学学院，河北省数学与交叉科学国际联合研究中心，河北省数学研究中心，河北省计算数学与应用重点实验室，河北 石家庄；朱泉龙, 李晓清*：中国石油大学理学院，北京
关键词: 排列；有禁模式；组合计数；Permutation； Pattern Avoidance； Combinatorial Enumeration
摘要: 本文首先介绍有禁排列相关的基本定义，对避免双3长vincular模式排列的计数结果进行整理，将计数结果相同的模式用表格的形式进行分类。随后我们使用特殊元素分析与位置分析这两种方法，给出等8个避免双3长vincular模式排列计数结果的代数证明。
Abstract: This article first introduces the basic definitions related to forbidden permutations, and summarizes the counting results of bivincular patterns of length 3. We classify patterns with the same counting results and present them intabular form. Additionally, we also provides algebraic proofs for the counting results of eight bivincular patterns of length 3, including , using two mainmethods: analysis of special elements and analysis of positions.
文章引用：赵沨, 朱泉龙, 李晓清. 避免双3长Vincular模式排列的计数研究[J]. 理论数学, 2023, 13(10): 3111-3118. https://doi.org/10.12677/PM.2023.1310322

参考文献

[1] Kitaev, S. (2011) Patterns in Permutations and Words. Springer, Heidelberg.
[2] Knuth, D.E. (1973) The Art of Computer Programming, Volume 3: Sorting and Searching. Pearson Education, India.
[3] Simion, R. and Schmidt, F.W. (1985) Restricted Permutations. European Journal of Combinatorics, 6, 383-406. [Google Scholar] [CrossRef] 
[4] Lewis, J.B. (2011) Pattern Avoidance for Alternating Per-mutations and Young Tableaux. Journal of Combinatorial Theory, Series A, 118, 1436-1450. [Google Scholar] [CrossRef] 
[5] Bloom, J.A. (2014) Refinement of Wilf-Equivalence for Patterns of Length 4. Journal of Combinatorial Theory, Series A, 124, 166-177. [Google Scholar] [CrossRef] 
[6] Kremer, D. and Shiu, W.C. (2003) Finite Transition Matrices for Permutations Avoiding Pairs of Length Four Patterns. Discrete Mathematics, 268, 171-183. [Google Scholar] [CrossRef] 
[7] Rotem, D. (1981) Stack Sortable Permutations. Discrete Mathematics, 33, 185-196. [Google Scholar] [CrossRef] 
[8] West, J. (1996) Generating Trees and Forbidden Subse-quences. Discrete Mathematics, 157, 363-372. [Google Scholar] [CrossRef] 
[9] Bóna, M. (1997) Exact Enumeration of 1342-Avoiding Permutations: A Close Link with Labeled Trees and Planar Maps. Journal of Combinatorial Theory, Series A, 80, 257-272. [Google Scholar] [CrossRef] 
[10] Babson, E. and Steingrímsson, E. (2000) Generalized Per-mutation Patterns and a Classification of the Mahonian Statistics. Séminaire Lotharingien de Combinatoire (Electronic Only), 44, 1-18.
[11] Claesson, A. (2001) Generalized Pattern Avoidance. European Journal of Combinatorics, 22, 961-971. [Google Scholar] [CrossRef] 
[12] Kitaev, S. (2003) Multi-Avoidance of Generalised Patterns. Discrete Mathematics, 260, 89-100. [Google Scholar] [CrossRef] 
[13] Elizalde, S. and Mansour, T. (2005) Restricted Motzkin Permutations, Motzkin Paths, Continued Fractions, and Chebyshev Polynomials. Discrete Mathematics, 305, 170-189. [Google Scholar] [CrossRef] 
[14] Barnabei, M., Bonetti, F. and Silimbani. M. (2010) The Joint Dis-tribution of Consecutive Patterns and Descents in Permutations Avoiding 3-1-2. European Journal of Combinatorics, 31, 1360-1371. [Google Scholar] [CrossRef] 
[15] 武蕊红. 排列组合中常见的问题及解题方法[J]. 山西师范大学学报: 自然科学版, 2013(S1): 5-6.
[16] Donaghey, R. and Shapiro, L.W. (1977) Motzkin Numbers. Journal of Com-binatorial Theory, Series A, 23, 291-301. [Google Scholar] [CrossRef] 

为你推荐