Continued fractions, statistics, and generalized patterns

Toufik Mansour

Continued fractions, statistics, and generalized patterns

Research output: Contribution to journal › Article › peer-review

Abstract

Recently, Babson and Steingrímsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Following [BCS], let e _kπ (respectively; f_kπ) be the number of the occurrences of the generalized pattern 12-3-...-k (respectively; 21-3-...-k) in π. In the present note, we study the distribution of the statistics e _kπ and f_kπ in a permutation avoiding the classical pattern 1-3-2. We also present some applications of our results which relate the enumeration of permutations avoiding the classical pattern 1-3-2 according to the statistics e_k and f_k to Narayana numbers and Catalan numbers.

Original language	English
Pages (from-to)	265-274
Number of pages	10
Journal	Ars Combinatoria
Volume	70
State	Published - Jan 2004
Externally published	Yes

ASJC Scopus subject areas

General Mathematics

Cite this

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AB - Recently, Babson and Steingrímsson (see [BS]) introduced generalized permutations patterns that allow the requirement that two adjacent letters in a pattern must be adjacent in the permutation. Following [BCS], let e kπ (respectively; fkπ) be the number of the occurrences of the generalized pattern 12-3-...-k (respectively; 21-3-...-k) in π. In the present note, we study the distribution of the statistics e kπ and fkπ in a permutation avoiding the classical pattern 1-3-2. We also present some applications of our results which relate the enumeration of permutations avoiding the classical pattern 1-3-2 according to the statistics ek and fk to Narayana numbers and Catalan numbers.

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ER -

Continued fractions, statistics, and generalized patterns

Abstract

ASJC Scopus subject areas

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