T. Mansour,孙怡东.避免$2$字母符号模式的具有偶数个符号的带符号排列[J].数学研究及应用,2009,29(5):813~822 |
避免$2$字母符号模式的具有偶数个符号的带符号排列 |
Even Signed Permutations Avoiding 2-Letter Signed Patterns |
投稿时间:2007-12-27 修订日期:2008-02-28 |
DOI:10.3770/j.issn:1000-341X.2009.05.006 |
中文关键词: 禁位模式 带符号排列 Catalan数. |
英文关键词:forbidden pattern signed permutation Catalan number. |
基金项目:国家自然科学基金(No.10801020). |
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中文摘要: |
设集合${\cal D}_n$表示$[n]=\{1, \dots, n\}$上的具有偶数个符号的带符号排列的全体, 集合${\cal D}_n(T)$表示避免$T$中所有模式的${\cal D}_n$中的带符号排列的全体. 本文刻画了当$T\subset B_2$时集合${\cal D}_n(T)$的元素个数, 这些计数序列包括二项式系数, Catalan数, Fibonacci数等. |
英文摘要: |
Let ${\cal D}_n$ be the set of all signed permutations on $[n]=\{1,\dots, n\}$ with even signs, and let ${\cal D}_n(T)$ be the set of all signed permutations in ${\cal D}_n$ which avoids a set $T$ of signed patterns. In this paper, we find all the cardinalities of the sets ${\cal D}_n(T)$ where $T\subseteq B_2$. Some of the cardinalities encountered involve inverse binomial coefficients, binomial coefficients, Catalan numbers, and Fibonacci numbers. |
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