Geodesic
Counterexamples to the Neggers-Stanley conjecture
Brändén, Petter1
1 Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden
Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 155-158 Cet article a éte moissonné depuis la source American Mathematical Society

Voir la notice de l'article

The Neggers-Stanley conjecture asserts that the polynomial counting the linear extensions of a labeled finite partially ordered set by the number of descents has real zeros only. We provide counterexamples to this conjecture.
DOI : 10.1090/S1079-6762-04-00140-4

Brändén, Petter 1

1 Department of Mathematics, Chalmers University of Technology and Göteborg University, S-412 96 Göteborg, Sweden 
@article{10_1090_S1079_6762_04_00140_4,
     author = {Br\"and\'en, Petter},
     title = {Counterexamples to the {Neggers-Stanley} conjecture},
     journal = {Electronic research announcements of the American Mathematical Society},
     pages = {155--158},
     year = {2004},
     volume = {10},
     doi = {10.1090/S1079-6762-04-00140-4},
     url = {http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00140-4/}
}
TY  - JOUR
AU  - Brändén, Petter
TI  - Counterexamples to the Neggers-Stanley conjecture
JO  - Electronic research announcements of the American Mathematical Society
PY  - 2004
SP  - 155
EP  - 158
VL  - 10
UR  - http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00140-4/
DO  - 10.1090/S1079-6762-04-00140-4
ID  - 10_1090_S1079_6762_04_00140_4
ER  - 
%0 Journal Article
%A Brändén, Petter
%T Counterexamples to the Neggers-Stanley conjecture
%J Electronic research announcements of the American Mathematical Society
%D 2004
%P 155-158
%V 10
%U http://geodesic.mathdoc.fr/articles/10.1090/S1079-6762-04-00140-4/
%R 10.1090/S1079-6762-04-00140-4
%F 10_1090_S1079_6762_04_00140_4
Brändén, Petter. Counterexamples to the Neggers-Stanley conjecture. Electronic research announcements of the American Mathematical Society, Tome 10 (2004), pp. 155-158. doi: 10.1090/S1079-6762-04-00140-4

[1] Brenti, Francesco Unimodal, log-concave and Pólya frequency sequences in combinatorics Mem. Amer. Math. Soc. 1989

[2] Harper, L. H. Stirling behavior is asymptotically normal Ann. Math. Statist. 1967 410 414

[3] Neggers, Joseph Representations of finite partially ordered sets J. Combin. Inform. System Sci. 1978 113 133

[4] Rahman, Q. I., Schmeisser, G. Analytic theory of polynomials 2002

[5] Simion, Rodica A multi-indexed Sturm sequence of polynomials and unimodality of certain combinatorial sequences J. Combin. Theory Ser. A 1984 15 22

[6] Stanley, Richard P. Ordered structures and partitions 1972

[7] Stanley, Richard P. Hilbert functions of graded algebras Advances in Math. 1978 57 83

[8] Stanley, Richard P. Combinatorics and commutative algebra 1996

[9] Wagner, David G. Enumeration of functions from posets to chains European J. Combin. 1992 313 324

Cité par Sources :