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Publications (10 of 35) Show all publications
Brändén, P., Leander, M. & Visontai, M. (2016). Multivariate Eulerian Polynomials and Exclusion Processes. Combinatorics, probability & computing, 25(4), 486-499
Open this publication in new window or tab >>Multivariate Eulerian Polynomials and Exclusion Processes
2016 (English)In: Combinatorics, probability & computing, ISSN 0963-5483, E-ISSN 1469-2163, Vol. 25, no 4, p. 486-499Article in journal (Refereed) Published
Abstract [en]

We give a new combinatorial interpretation of the stationary distribution of the (partially) asymmetric exclusion process on a finite number of sites in terms of decorated alternative trees and coloured permutations. The corresponding expressions of the multivariate partition functions are then related to multivariate generalisations of Eulerian polynomials for coloured permutations considered recently by N. Williams and the third author, and others. We also discuss stability and negative dependence properties satisfied by the partition functions.

Place, publisher, year, edition, pages
Cambridge University Press, 2016
Keywords
Probability, Asymmetric exclusion process, Dependence properties, Eulerian polynomial, Exclusion process, Finite number, Partition functions, Stationary distribution, Williams
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-187219 (URN)10.1017/S0963548316000031 (DOI)000377906700001 ()2-s2.0-84961214714 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20160719

Available from: 2016-05-18 Created: 2016-05-18 Last updated: 2017-11-30Bibliographically approved
Brändén, P. & Chasse, M. (2015). Infinite log-concavity for polynomial pólya frequency sequences. Proceedings of the American Mathematical Society, 143(12), 5147-5158
Open this publication in new window or tab >>Infinite log-concavity for polynomial pólya frequency sequences
2015 (English)In: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 143, no 12, p. 5147-5158Article in journal (Refereed) Published
Abstract [en]

McNamara and Sagan conjectured that if a0, a1, a2, . . . is a Pólya frequency (PF) sequence, then so is (formula presented), . . .. We prove this conjecture for a natural class of PF-sequences which are interpolated by polynomials. In particular, this proves that the columns of Pascal’s triangle are infinitely log-concave, as conjectured by McNamara and Sagan. We also give counterexamples to the first mentioned conjecture. Our methods provide families of nonlinear operators that preserve the property of having only real and nonpositive zeros.

Place, publisher, year, edition, pages
American Mathematical Society (AMS), 2015
Keywords
Infinite log-concavity, Log-concavity, Pólya frequency sequence, Real zeros
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-181260 (URN)10.1090/proc/12654 (DOI)000364413200011 ()2-s2.0-84944198620 (Scopus ID)
Note

QC 20160205

Available from: 2016-02-05 Created: 2016-01-29 Last updated: 2017-11-30Bibliographically approved
Brändén, P. & Ottergren, E. (2014). A Characterization of Multiplier Sequences for Generalized Laguerre Bases. Constructive approximation, 39(3), 585-596
Open this publication in new window or tab >>A Characterization of Multiplier Sequences for Generalized Laguerre Bases
2014 (English)In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940, Vol. 39, no 3, p. 585-596Article in journal (Refereed) Published
Abstract [en]

We give a complete characterization of multiplier sequences for generalized Laguerre bases. We also apply our methods to give a short proof of the characterization of Hermite multiplier sequences achieved by Piotrowski.

Keywords
Multiplier sequences, Generalized Laguerre polynomials, Zeros of entire functions, Linear operators on polynomial spaces
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-147025 (URN)10.1007/s00365-013-9204-4 (DOI)000336274800007 ()2-s2.0-84901237875 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20140624

Available from: 2014-06-24 Created: 2014-06-23 Last updated: 2017-12-05Bibliographically approved
Brändén, P. (2014). Hyperbolicity cones of elementary symmetric polynomials are spectrahedral. Optimization Letters, 8(5), 1773-1782
Open this publication in new window or tab >>Hyperbolicity cones of elementary symmetric polynomials are spectrahedral
2014 (English)In: Optimization Letters, ISSN 1862-4472, E-ISSN 1862-4480, Vol. 8, no 5, p. 1773-1782Article in journal (Refereed) Published
Abstract [en]

We prove that the hyperbolicity cones of elementary symmetric polynomials are spectrahedral, i.e., they are slices of the cone of positive semidefinite matrices. The proof uses the matrix-tree theorem, an idea already present in Choe et al.

Keywords
Hyperbolic polynomials, Hyperbolicity cones, Spectrahedral cones, Elementary symmetric polynomials, Matrix-tree theorem
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-149990 (URN)10.1007/s11590-013-0694-6 (DOI)000339820400014 ()2-s2.0-84901616105 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20140901

Available from: 2014-09-01 Created: 2014-08-29 Last updated: 2017-12-05Bibliographically approved
Brändén, P. (2014). The Lee-Yang and Pólya-Schur programs. III. Zero-preservers on Bargmann-Fock spaces. American Journal of Mathematics, 136(1), 241-253
Open this publication in new window or tab >>The Lee-Yang and Pólya-Schur programs. III. Zero-preservers on Bargmann-Fock spaces
2014 (English)In: American Journal of Mathematics, ISSN 0002-9327, E-ISSN 1080-6377, Vol. 136, no 1, p. 241-253Article in journal (Refereed) Published
Abstract [en]

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.

Keywords
Sequences, Theorems
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-142986 (URN)10.1353/ajm.2014.0003 (DOI)000331339600009 ()2-s2.0-84892850369 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20140314

Available from: 2014-03-14 Created: 2014-03-14 Last updated: 2017-12-05Bibliographically approved
Bränden, P. & Moci, L. (2014). The multivariate arithmetic Tutte polynomial. Transactions of the American Mathematical Society, 366(10), 5523-5540
Open this publication in new window or tab >>The multivariate arithmetic Tutte polynomial
2014 (English)In: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 366, no 10, p. 5523-5540Article in journal (Refereed) Published
Abstract [en]

We introduce an arithmetic version of the multivariate Tutte polynomial and a quasi-polynomial that interpolates between the two. A generalized Fortuin-Kasteleyn representation with applications to arithmetic colorings and flows is obtained. We give a new and more general proof of the positivity of the coefficients of the arithmetic Tutte polynomial and (in the representable case) a geometrical interpretation of them.

Keywords
Tutte polynomial, multivariate Tutte polynomial, Potts model, toric arrangement, chromatic polynomial, matroid, arithmetic matroid, abelian group, quasi-polynomial
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-158844 (URN)10.1090/S0002-9947-2014-06092-3 (DOI)000344826100017 ()2-s2.0-84924785538 (Scopus ID)
Funder
Knut and Alice Wallenberg Foundation
Note

QC 20150122

Available from: 2015-01-22 Created: 2015-01-12 Last updated: 2017-12-05Bibliographically approved
Brändén, P. & Jonasson, J. (2012). Negative Dependence in Sampling. Scandinavian Journal of Statistics, 39(4), 830-838
Open this publication in new window or tab >>Negative Dependence in Sampling
2012 (English)In: Scandinavian Journal of Statistics, ISSN 0303-6898, E-ISSN 1467-9469, Vol. 39, no 4, p. 830-838Article in journal (Refereed) Published
Abstract [en]

. The strong Rayleigh property is a new and robust negative dependence property that implies negative association; in fact it implies conditional negative association closed under external fields (CNA+). Suppose that and are two families of 0-1 random variables that satisfy the strong Rayleigh property and let . We show that {Zi} conditioned on is also strongly Rayleigh; this turns out to be an easy consequence of the results on preservation of stability of polynomials of Borcea & Branden (Invent. Math., 177, 2009, 521569). This entails that a number of important pps sampling algorithms, including Sampford sampling and Pareto sampling, are CNA+. As a consequence, statistics based on such samples automatically satisfy a version of the Central Limit Theorem for triangular arrays.

Keywords
Pareto sampling, Rayleigh property, Sampford sampling, uniform spanning tree
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-109178 (URN)10.1111/j.1467-9469.2011.00766.x (DOI)000311396200016 ()2-s2.0-84870063383 (Scopus ID)
Funder
Knut and Alice Wallenberg FoundationSwedish Research Council
Note

QC 20121307

Available from: 2013-01-07 Created: 2012-12-21 Last updated: 2017-12-06Bibliographically approved
Brändén, P. (2012). Solutions to two problems on permanents. Linear Algebra and its Applications, 436(1), 53-58
Open this publication in new window or tab >>Solutions to two problems on permanents
2012 (English)In: Linear Algebra and its Applications, ISSN 0024-3795, E-ISSN 1873-1856, Vol. 436, no 1, p. 53-58Article in journal (Refereed) Published
Abstract [en]

In this note we settle two open problems in the theory of permanents by using recent results from other areas of mathematics. Both problems were recently discussed in Bapat's survey [2]. Bapat conjectured that certain quotients of permanents, which generalize symmetric function means, are concave. We prove this conjecture by using concavity properties of hyperbolic polynomials. Motivated by problems on random point processes, Shirai and Takahashi raised the problem: Determine all real numbers a for which the alpha-permanent (or alpha-determinant) is nonnegative for all positive semidefinite matrices. We give a complete solution to this problem by using recent results of Scott and Sokal on completely monotone functions. It turns out that the conjectured answer to the problem is false.

Keywords
Permanent, alpha-Permanent, alpha-Determinant, Positivity, Hyperbolic polynomial, Complete monotonicity, Symmetric function mean
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-53388 (URN)10.1016/j.laa.2011.06.022 (DOI)000297431200005 ()2-s2.0-80055063559 (Scopus ID)
Note
QC 20111228Available from: 2011-12-28 Created: 2011-12-28 Last updated: 2017-12-08Bibliographically approved
Brändén, P. & Moci, L. (2012). The multivariate arithmetic Tutte polynomial. Paper presented at 24th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2012; Nagoya; Japan; 30 July 2012 through 3 August 2012. Discrete Mathematics & Theoretical Computer Science, 661-672
Open this publication in new window or tab >>The multivariate arithmetic Tutte polynomial
2012 (English)In: Discrete Mathematics & Theoretical Computer Science, ISSN 1462-7264, E-ISSN 1365-8050, p. 661-672Article in journal (Refereed) Published
Abstract [en]

We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two. We provide a generalized Fortuin-Kasteleyn representation for representable arithmetic matroids, with applications to arithmetic colorings and flows. We give a new proof of the positivity of the coefficients of the arithmetic Tutte polynomial in the more general framework of pseudo-arithmetic matroids. In the case of a representable arithmetic matroid, we provide a geometric interpretation of the coefficients of the arithmetic Tutte polynomial.

Keywords
Abelian groups, Arithmetic matroids, Chromatic polynomial, Matroids, Potts model, Tutte polynomial
National Category
Mathematics Computer and Information Sciences
Identifiers
urn:nbn:se:kth:diva-144779 (URN)2-s2.0-84887518992 (Scopus ID)
Conference
24th International Conference on Formal Power Series and Algebraic Combinatorics, FPSAC 2012; Nagoya; Japan; 30 July 2012 through 3 August 2012
Note

QC 20140505

Available from: 2014-05-05 Created: 2014-04-29 Last updated: 2018-01-11Bibliographically approved
Brändén, P. (2011). A generalization of the Heine-Stieltjes theorem. Constructive approximation, 34(1), 135-148
Open this publication in new window or tab >>A generalization of the Heine-Stieltjes theorem
2011 (English)In: Constructive approximation, ISSN 0176-4276, E-ISSN 1432-0940, Vol. 34, no 1, p. 135-148Article in journal (Refereed) Published
Abstract [en]

The Heine-Stieltjes theorem describes the polynomial solutions, (v,f) such that T(f)=vf, to specific second-order differential operators, T, with polynomial coefficients. We extend the theorem to concern all (nondegenerate) differential operators preserving the property of having only real zeros, thus solving a conjecture of B. Shapiro. The new methods developed are used to describe intricate interlacing relations between the zeros of different pairs of solutions. This extends recent results of Bourget, McMillen and Vargas for the Heun equation and answers their question of how to generalize their results to higher degrees. Many of the results are new even for the classical case.

Keywords
Heine-Stieltjes theorem, Heine-Stieltjes polynomials, Van Vleck polynomials, Hyperbolic polynomials, Real zeros, Interlacing zeros
National Category
Mathematics
Identifiers
urn:nbn:se:kth:diva-78682 (URN)10.1007/s00365-010-9102-y (DOI)000290805700006 ()
Note
QC 20120221Available from: 2012-02-08 Created: 2012-02-08 Last updated: 2017-12-08Bibliographically approved
Organisations
Identifiers
ORCID iD: ORCID iD iconorcid.org/0000-0003-1055-1474

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