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- Bränden, Petter, et al.
(författare)
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Catalan continued fractions, and increasing subsequences in permutations
- 2002
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Ingår i: Discrete Mathematics. - 0012-365X .- 1872-681X. ; 258:03-jan, s. 275-287
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Tidskriftsartikel (refereegranskat)abstract
- We call a Stieltjes continued fraction with monic monomial numerators a Catalan continued fraction. Let e(k)(pi) be the number of increasing subsequences of length k + 1 in the permutation pi. We prove that any Catalan continued fraction is the multivariate generating function of a family of statistics on the 132-avoiding permutations, each consisting of a (possibly infinite) linear combination of the e(k)S. Moreover, there is an invertible linear transformation that translates between linear combinations of ekS and the corresponding continued fractions. Some applications are given, one of which relates fountains of coins to 132-avoiding permutations according to number of inversions. Another relates ballot numbers to such permutations according to number of right-to-left maxima.
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| 2. |
- Bränden, Petter
(författare)
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q-Narayana numbers and the flag h-vector
- 2004
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Ingår i: Discrete Mathematics. - : Elsevier BV. - 0012-365X .- 1872-681X. ; 281:03-jan, s. 67-81
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Tidskriftsartikel (refereegranskat)abstract
- The Narayana numbers are N(n,k) = (1/n)((n)(k))((n)(k+1)). There are several natural statistics on Dyck paths with a distribution given by N(n, k). We show the equidistribution of Narayana statistics by computing the flag h-vector of J(2 x n) in different ways. In the process we discover new Narayana statistics and provide co-statistics for the Narayana statistics so that the bi-statistics have a distribution given by Furlinger and Hofbauer's q-Narayana numbers. We interpret the flag h-vector in terms of semi-standard Young tableaux, which enables us to express the q-Narayana numbers in terms of Schur functions. We also introduce what we call pre-shellings of simplicial complexes.
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