Even Signed Permutations Avoiding 2-Letter Signed Patterns
Received:December 27, 2007  Revised:February 28, 2008
Key Word: forbidden pattern   signed permutation   Catalan number.
Fund ProjectL:the National Natural Science Foundation of China (No.10801020).
 Author Name Affiliation MANSOUR Toufik Department of Mathematics, Haifa University, Haifa 31905, Israel SUN Yi Dong Department of Mathematics, Dalian Maritime University, Liaoning 116026, China
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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.