ON LINEAR TRANSFORMATIONS PRESERVING THE PÓLYA FREQUENCY PROPERTY

ON LINEAR TRANSFORMATIONS PRESERVING THE PÓLYA FREQUENCY PROPERTY

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by Petter Brändén

Citations:

14 - 3 self

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@MISC{Brändén_onlinear,
    author = {Petter Brändén},
    title = {ON LINEAR TRANSFORMATIONS PRESERVING THE PÓLYA FREQUENCY PROPERTY },
    year = {}
}

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Abstract

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.

Citations

675	RP: Enumerative Combinatorics I - Stanley - 1997
112	E.D.,1971 Special functions - Rainville
93	Log-concave and unimodal sequences in algebra, combinatorics, and geometry - Stanley - 1989
76	Théorie géométrique des polynômes eulériens - Foata, Schützenberger - 1970
67	Theory of monomerdimer systems - Heilmann, Lieb - 1972
61	log-concave and Pólya frequency sequences in combinatorics - Brenti, Unimodal - 1989
55	Root systems and generalized associahedra - Fomin, Reading - 2005
48	Log-concave and unimodal sequences in algebra, combinatorics, and geometry: an update - Brenti - 1994
36	q-Eulerian polynomials arising from Coxeter groups - Brenti - 1994
36	Positivity problems and conjectures in algebraic combinatorics - Stanley - 2000
31	Verteilung und Berechnung der Nullstellen Reeller Polynome. VEB. Deutscher Verlag der Wissenchaften Band 55 - Obreschkoff - 1963
27	On the Charney-Davis and Neggers-Stanley conjectures - Reiner, Welker
20	A Survey of Stack-Sorting Disciplines - Bóna
19	Raney paths and a combinatorial relationship between rooted nonseparable planar maps and two-stack-sortable permutations - Goulden, West - 1996
18	The Narayana distribution - Sulanke - 1975
18	Total positivity of Hadamard products - Wagner - 1992
17	On the generating function of totally positive sequences - Edrei - 1952
16	Multi-statistic enumeration of two-stack sortable permutations, Electron - Bousquet-Mélou - 1998
16	A Bijective Census of Nonseparable Planar Maps - Jacquard, Schaeffer - 1998
14	Descents and one-dimensional characters for classical Weyl groups - Reiner - 1995
14	Some permutation representations of Weyl groups associated with the cohomology of toric varieties - Stembridge - 1994
13	Enumeration of functions from posets to chains - Wagner - 1992
12	Location of zeros of chromatic and related polynomials of graphs, Canad - Brenti, Royle, et al. - 1994
12	Multiplier sequences for fields - Craven, Csordas - 1977
12	Geometry of polynomials. Second edition - Marden - 1966
12	The partition polynomials of a finite set system - Wagner - 1991
10	A combinatorial proof - Dulucq, Gire, et al. - 1998
9	Corrigendum: ”Symmetry and unimodality in t-stack sortable permutations - Bóna
9	Obreshkoff’s theorem revisited: What convex sets are contained in the set of hyperbolic polynomials - Dedieu - 1992
9	Hadamard products of stable polynomials are stable, Journal of mathematical analysis and applications 202 - Garloff, Wagner - 1996
8	A class of q-symmetric functions arising from plethysm - Brenti - 2000
8	Zwei Sätze über algebraische Gleichungen mit lauter reelen Wurzeln (In German). [Two theorems on algebraic equations with only real roots.] Journal für reine und angew - Schur - 1914
7	The generating function of two-stack sortable permutations by descents is real-rooted, arXiv: math.CO/0303149 - Brändén
7	Advanced combinatorics. D. Reidel Publishing Co., Dordrecht, enlarged edition - Comtet - 1974
6	On operators on polynomials preserving real-rootedness and the Neggers-Stanley conjecture - Brändén
3	Collected Papers - Pólya - 1974