Lattice paths and Kazhdan-Lusztig polynomials

Journal of the American Mathematical Society

Volumn 11, Issue 2, 1998, Pages 229-259

  Brenti, Francesco ^a  

^a UNIVERSITY OF ROME TOR VERGATA   (Italy)

Author keywords

Bayer Billera relations; Bruhat order; Coxeter group; Eulerian poset; Generalized h vector; Kazhdan Lusztig polynomial; Lattice path

Indexed keywords

EID: 0347392841     PISSN: 08940347     EISSN: None     Source Type: Journal    
DOI: 10.1090/s0894-0347-98-00249-5     Document Type: Article

References (24)

1. D. André, Solution directe du probléme résolu par M. Bertrand, C. R. Acad. Sci. Paris 105 (1887), 436-437.
2. M. M. Bayer and L. J. Billera, Generalized Dehn-Sommerville relations for polytopes, spheres and Eulerian partially ordered sets, Invent. Math. 79 (1985), 143-157. MR 86f:52010b
3. A. Björner, A. Garsia, and R. Stanley, An introduction to Cohen-Macaulay partially ordered sets, in Ordered Sets (I. Rival, Editor), Reidal, Dordrecht/Boston, 1982, 583-615. MR 83i:06001
4. A. Björner and M. Wachs, Bruhat order of Coxeter groups and shellability, Adv. in Math. 43 (1982), 87-100. MR 83i:20043
5. A. Björner, Orderings of Coxeter groups, Combinatorics and Algebra, Contemporary Math., vol. 34, Amer. Math. Soc., 1984, 175-195. MR 86i:05024
6. F. Brenti, A combinatorial formula for Kazhdan-Lusztig polynomials, Invent. Math. 118 (1994), 371-394. MR 96c:20074
7. F. Brenti, Combinatorial expansions of Kazhdan-Lusztig polynomials, J. London Math. Soc. (2) 55 (1997), 448-472. CMP 97:13
8. F. Brenti, Kazhdan-Lusztig and R-polynomials from a combinatorial point of view, Discrete Math., to appear.
9. L. Comtet, Advanced Combinatorics, Reidel, Dordrecht/Boston, 1974. MR 57:124
10. V. V. Deodhar, Some characterizations of Bruhat ordering on a Coxeter group and determination of the relative Möbius function, Invent. Math. 39 (1977), 187-198. MR 55:8209
11. V. V. Deodhar, On some geometric aspects of Bruhat orderings. I. A finer decomposition of Bruhat cells, Invent. Math. 79 (1985), 499-511. MR 86f:20045
12. M. Dyer, Hecke algebras and reflections in Coxeter groups, Ph. D. Thesis, University of Sydney, 1987.
13. M. Dyer, On the "Bruhat graph" of a Coxeter system, Comp. Math. 78 (1991), 185-191. MR 92c:20076
14. M. Dyer, Hecke algebras and shellings of Bruhat intervals, Comp. Math. 89 (1993), 91-115. MR 95c:20053
15. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, Wiley, New York, 1950. MR 12:424a
16. I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley-Interscience, New York, 1983. MR 84m:05002
17. J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics, no.29, Cambridge Univ. Press, Cambridge, 1990. MR 92h:20002
18. D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 81j:20066
19. D. Kazhdan and G. Lusztig, Schubert varieties and Poincaré duality, Geometry of the Laplace operator, Proc. Sympos. Pure Math. 34, Amer. Math. Soc., Providence, RI, 1980, pp. 185-203. MR 84g:14054
20. R. P. Stanley, Enumerative Combinatorics, vol.1, Wadsworth and Brooks/Cole, Monterey, CA, 1986. MR 87j:05003
21. R. P. Stanley, Generalized h-vectors, intersection cohomology of toric varieties, and related results, Adv. Studies Pure Math. 11 (1987), 187-213. MR 89f:52016
22. R. P. Stanley, Log-concave and unimodal sequences in Algebra, Combinatorics and Geometry, Annals of the New York Academy of Sciences 576 (1989), 500-534. MR 92e:05124
23. R. P. Stanley, Subdivisions and local h-vectors, J. Amer. Math. Soc. 5 (1992), 805-851. MR 93b:52012
24. D.-N. Verma, Möbius inversion for the Bruhat order on a Weyl group, Ann. Sci. École Norm. Sup. 4 (1971), 393-398. MR 45:139