On the Number of Permutations Avoiding a Given Pattern
نویسندگان
چکیده
منابع مشابه
On the Number of Permutations Avoiding a Given Pattern
Let σ ∈ Sk and τ ∈ Sn be permutations. We say τ contains σ if there exist 1 ≤ x1 < x2 < . . . < xk ≤ n such that τ(xi) < τ(xj) if and only if σ(i) < σ(j). If τ does not contain σ we say τ avoids σ. Let F (n, σ) = |{τ ∈ Sn| τ avoids σ}|. Stanley and Wilf conjectured that for any σ ∈ Sk there exists a constant c = c(σ) such that F (n, σ) ≤ cn for all n. Here we prove the following weaker statemen...
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Let 2 S k and 2 S n be permutations. We say contains if there exist 1 x 1 < x 2 < : : : < x k n such that (x i) < (x j) if and only if (i) < (j). If does not contain we say avoids. Let F (n;) = jf 2 S n j avoids gj. Stanley and Wilf conjectured that for any 2 S k there exists a constant c = c() such that F (n;) c n for all n. Here we prove the following weaker statement: For every xed 2 S k , F...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3002