Petter Brändén

Learn More
Any permutation statistic f : S → C may be represented uniquely as a, possibly infinite, linear combination of (classical) permutation patterns: f = Στλf (τ)τ . To provide explicit expansions for certain statistics, we introduce a new type of permutation patterns that we call mesh patterns. Intuitively, an occurrence of the mesh pattern p = (π,R) is an(More)
We say that a word w on a totally ordered alphabet avoids the word v if there are no subsequences in w order-equivalent to v. In this paper we suggest a new approach to the enumeration of words on at most k letters avoiding a given pattern. By studying an automaton which for fixed k generates the words avoiding a given pattern we derive several previously(More)
We study the effect on the zeros of generating functions of sequences under certain non-linear transformations. Characterizations of Pólya– Schur type are given of the transformations that preserve the property of having only real and non-positive zeros. In particular, if a polynomial a0 + a1z + · · · + anzn has only real and non-positive zeros, then so(More)
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×n) in different ways. In the process we discover new Narayana statistics and provide co-statistics for which the Narayana(More)
We generalize the notion of graded posets to what we call sign-graded (labeled) posets. We prove that the W -polynomial of a sign-graded poset is symmetric and unimodal. This extends a recent result of Reiner and Welker who proved it for graded posets by associating a simplicial polytopal sphere to each graded poset. By proving that the W -polynomials of(More)
We call a Stieltjes continued fraction with monic monomial numerators a Catalan continued fraction. Let ek(π) be the number of increasing subsequences of length k + 1 in the permutation π. 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(More)