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Exact Enumeration Of 1342Avoiding Permutations A Close Link With Labeled Trees And Planar Maps
, 1997
"... Solving the first nonmonotonic, longerthanthree instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342avoiding permutations of length n as well as an exact formula for their number Sn (1342). While achieving this, we bijectively prove that the number of inde ..."
Abstract

Cited by 84 (7 self)
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Solving the first nonmonotonic, longerthanthree instance of a classic enumeration problem, we obtain the generating function H(x) of all 1342avoiding permutations of length n as well as an exact formula for their number Sn (1342). While achieving this, we bijectively prove that the number of indecomposable 1342avoiding permutations of length n equals that of labeled plane trees of a certain type on n vertices recently enumerated by Cori, Jacquard and Schaeffer, which is in turn known to be equal to the number of rooted bicubic maps enumerated by Tutte in 1963. Moreover, H(x) turns out to be algebraic, proving the first nonmonotonic, longerthanthree instance of a conjecture of Zeilberger and Noonan. We also prove that n p Sn (1342) converges to 8, so in particular, limn!1 (Sn (1342)=Sn (1234)) = 0.
Counting occurrences of some subword patterns
 Discr. Math. Theor. Comp. Sci
"... Abstract. We find generating functions for the number of strings (words) containing a specified number of occurrences of certain types of orderisomorphic classes of substrings called subword patterns. In particular, we find generating functions for the number of strings containing a specified numbe ..."
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Cited by 14 (9 self)
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Abstract. We find generating functions for the number of strings (words) containing a specified number of occurrences of certain types of orderisomorphic classes of substrings called subword patterns. In particular, we find generating functions for the number of strings containing a specified number of occurrences of a given 3letter subword pattern. 1.
A generalization of SimionSchmidt's bijection for restricted permutations
 Paper #R14
, 2003
"... We consider the two permutation statistics which count the distinct pairs obtained from the nal two terms of occurrences of patterns 1 m 2 m(m 1) and 1 m 2 (m 1)m in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution o ..."
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Cited by 4 (0 self)
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We consider the two permutation statistics which count the distinct pairs obtained from the nal two terms of occurrences of patterns 1 m 2 m(m 1) and 1 m 2 (m 1)m in a permutation, respectively. By a simple involution in terms of permutation diagrams we will prove their equidistribution over the symmetric group. As a special case we derive a onetoone correspondence between permutations which avoid each of the patterns 1 m 2 m(m 1) 2 Sm and those which avoid each of the patterns 1 m 2 (m 1)m 2 Sm . For m = 3 this correspondence coincides with the bijection given by Simion and Schmidt in [11].