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- PETTER BRÄNDÉN
- 2004

We prove that certain linear operators preserve the Pólya frequency property and real-rootedness, and apply our results to settle some conjectures and open problems in combinatorics proposed by Bóna, Brenti and Reiner-Welker.

- Petter Brändén, Anders Claesson
- Electr. J. Comb.
- 2011

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)

- Petter Brändén, Toufik Mansour
- J. Comb. Theory, Ser. A
- 2005

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)

- PETTER BRÄNDÉN
- 2013

We characterize linear operators preserving zero-restrictions on entire functions in weighted Bargmann–Fock spaces. This extends the characterization of linear operators on polynomials preserving stability (due to Borcea and the author) to the realm of entire functions, and translates into an optimal, albeit formal, Lee–Yang theorem.

- PETTER BRÄNDÉN
- 2009

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)

- Petter Brändén
- Eur. J. Comb.
- 2008

We study a group action on permutations due to Foata and Strehl and use it to prove that the descent generating polynomial of certain sets of permutations has a nonnegative expansion in the basis {t(1 + t)} i=0 , m = ⌊(n−1)/2⌋. This property implies symmetry and unimodality. We prove that the action is invariant under stack-sorting which strengthens recent… (More)

- Petter Brändén
- Discrete Mathematics
- 2004

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)

- Petter Brändén
- Optimization Letters
- 2014

- Petter Brändén
- Electr. J. Comb.
- 2004

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)

- Petter Brändén, Anders Claesson, Einar Steingrímsson
- Discrete Mathematics
- 2002

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)