| 避免$2$字母符号模式的具有偶数个符号的带符号排列 |
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| 引用本文： | 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. |
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| 作者姓名： | T. Mansour 孙怡东 |
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| 作者单位： | 海法大学数学系, 以色列 海法 31905;大连海事大学数学系, 辽宁 大连 116026 |
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| 基金项目： | 国家自然科学基金(No.10801020). |
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| 摘 要： | Let Dn be the set of all signed permutations on n] = {1,... ,n} with even signs, and let ：Dn（T） be the set of all signed permutations in Dn which avoids a set T of signed patterns. In this paper, we find all the cardinalities of the sets Dn（T） where T B2. Some of the cardinalities encountered involve inverse binomial coefficients, binomial coefficients, Catalan numbers, and Fibonacci numbers.
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| 关 键 词： | Fibonacci数 二项式系数 名模 字母 置换 签名 肾病 集合 |
| 收稿时间： | 2007/12/27 0:00:00 |
| 修稿时间： | 2008/2/28 0:00:00 |
Even Signed Permutations Avoiding 2-Letter Signed Patterns |
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| MANSOUR Toufik and SUN Yi Dong.Even Signed Permutations Avoiding 2-Letter Signed Patterns[J].Journal of Mathematical Research with Applications,2009,29(5):813-822. |
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| Authors: | MANSOUR Toufik and SUN Yi Dong |
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| Institution: | Department of Mathematics, Haifa University, Haifa 31905, Israel;Department of Mathematics, Dalian Maritime University, Liaoning 116026, China |
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| Abstract: | 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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| Keywords: | forbidden pattern signed permutation Catalan number |
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