On operators on polynomials preserving real-rootedness and the neggers-stanley conjecture

Journal of Algebraic Combinatorics

Volumn 20, Issue 2, 2004, Pages 119-130

  Brändén, Petter ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

Neggers stanley conjecture; Real rooted polynomials; Sturm sequence

Indexed keywords

FUNCTIONS; MATHEMATICAL OPERATORS; MATHEMATICAL TECHNIQUES; MATRIX ALGEBRA; THEOREM PROVING;

FERRERS POSETS; NEGGERS-STANLEY CONJECTURE; REAL-ROOTED POLYNOMIALS; STURM SEQUENCE;

POLYNOMIALS;

EID: 9144230821     PISSN: 09259899     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JACO.0000047295.93525.df     Document Type: Article

References (15)

1. F. Brenti, "Unimodal, log-concave and Pólya frequency sequences in combinatorics," Mem. Amer. Math. Soc 81(413) (1989), viii+106.
2. J. Dedieu, "Obreschkoff's theorem revisited: What convex sets are contained in the set of hyperbolic polynomials?" J. Pure Appl. Algebra 81(3) (1992), 269-278.
3. C.D. Godsil, Algebraic Combinatorics. Chapman and Hall Mathematics Series. Chapman & Hall. New York, 1993.
4. G.H. Hardy, J.E. Lilllewood, und G. Pólya. Inequalities, 2nd ed., Cambridge, at the University Press, 1952.
5. O.J. Heilmann and H.H. Lieb, "Theory of monomer-dimer systems, " Comm. Math. Phys. 25 (1972), 190-232.
6. B.J. Levin, Distribution of Zeros of Entire Functions. American Mathematical Society, Providence, R.I., 1964.
7. M. Marden. Geometry of Polynomials, 2nd edition, Mathematical Surveys, No. 3. American Mathematical Society, Providence, R.I., 1966.
8. A. Nijenhuis, "On permanents and the zeros of rook polynomials," J. Combinatorial Theory Ser. A 21(2) (1976), 240-244.
9. N. Obreschkoff, Verteilung und Berechnung der Nullstellen reeller Polynome, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963.
10. V. Reiner and V. Welker, "On the Charney-Davis and the Neggers-Stanley conjectures," http://www.math.umn.edu/~reiner/Papers/papers.html, 2002.
11. J. Schur, "Zwei sätze über algebraische gleichungen mit lauter reellen wurzeln," J. Reine Angew. Math. 144(2) (1914), 75-88.
12. R. Simion, "A multi-indexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences," J. Combin. Theory Ser. A 36(1) (1984), 15-22.
13. R.P. Stanley, Enumerative Combinatorics. vol. 2, volume 62 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, 1999.
14. D.G. Wagner, "Enumeration of functions from posets to chains," European J. Combin. 13(4) (1992), 313-324.
15. D.G. Wagner, "Total positivity of hadamard products," J. Math. Anal. Appl. 163(2) (1992), 459-483.