On a refinement of the generalized Catalan numbers for Weyl groups

Transactions of the American Mathematical Society

Volumn 357, Issue 1, 2005, Pages 179-196

  Athanasiadis, Christos A ^a  

^a UNIVERSITY OF CRETE   (Greece)

Author keywords

Coroot lattice; Hyperplane arrangements; Ideals; Narayana numbers; Regions; Root order; Weyl group

Indexed keywords

EID: 12844277556     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-04-03548-2     Document Type: Article

References (24)

1. C.A. Athanasiadis, Deformations of Coxeter hyperplane arrangements and their characteristic polynomials, in "Arrangements - Tokyo 1998" (M. Falk and H. Terao, eds.), Adv. Stud. Pure Math. 27, Kinokuniya, Tokyo, 2000, pp. 1-26. MR 2001i:52035
2. C.A. Athanasiadis, Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes, Bull. London Math. Soc. (to appear).
3. D. Bessis, The dual braid monoid, Ann. Sci. Ecole Norm. Sup. 36 (2003), 647-683.
4. P. Cellini and P. Papi, ad-nilpotent ideals of a Borel subalgebra, J. Algebra 225 (2000), 130-141. MR 2001g:17017
5. P. Cellini and P. Papi, ad-nilpotent ideals of a Borel subalgebra II, J. Algebra 258 (2002), 112-121.
6. F. Chapoton, S. Fomin and A.V. Zelevinsky, Polytopal realizations of generalized associahedra, Canad. Math. Bull. 45 (2002), 537-566. MR 2003j:52014
7. D.Ž. Djoković, On conjugacy classes of elements of finite order in compact or complex semisimple Lie groups, Proc. Amer. Math. Soc. 80 (1980), 181-184. MR 81b:20052
8. S. Fomin and A.V. Zelevinsky, Y-systems and generalized associahedra, Ann. of Math. 158 (2003), 977-1018.
9. S. Fomin and A.V. Zelevinsky, Cluster algebras II: finite type classification, Invent. Math. 154 (2003), 63-121.
10. M.D. Haiman, Conjectures on the quotient ring by diagonal invariants, J. Algebraic Combin. 3 (1994), 17-76. MR 95a:20014
11. J.E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge, England, 1990. MR 92h:20002
12. T. Venkata Narayana, Sur les treillis formés par les partitions d'un entier et leurs applications á la théorie des probabilités, Comp. Rend. Acad. Sci. Paris 240 (1955), 1188-1189. MR 17:14a
13. T. Venkata Narayana, Lattice path combinatorics with statistical applications, University of Toronto Press, 1979. MR 81f:60019
14. D.I. Panyushev, Ad-nilpotent ideals of a Borel subalgebra: generators and duality, J. Algebra (to appear).
15. M. Picantin, Explicit presentations for the dual braid monoids, C. R. Math. Acad. Sci. Paris Sér. I Math. 334 (2002), 843-848. MR 2003d:20046
16. A. Postnikov and R.P. Stanley, Deformations of Coxeter hyperplane arrangements, J. Combin. Theory Ser. A 91 (2000), 544-597. MR 2003g:52032
17. V. Reiner, Non-crossing partitions for classical reflection groups, Discrete Math. 177 (1997), 195-222. MR 99f:06005
18. V. Reiner and V. Welker, On the Charney-Davis and Neggers-Stanley conjectures, preprint, 2002, 38 pages.
19. J.-Y. Shi, Alcoves corresponding to an affine Weyl group, J. London Math. Soc. 35 (1987), 42-55. MR 88g:20103a
20. J.-Y. Shi, Sign types corresponding to an affine Weyl group, J. London Math. Soc. 35 (1987), 56-74. MR 88g:20103b
21. J.-Y. Shi, The number of ⊕-sign types, Quart. J. Math. Oxford Ser. (2) 48 (1997), 93-105. MR 98c:20080
22. E. Sommers, B-stable ideals in the nilradical of a Borel subalgebra, ArXiV preprint math.RT/0303182, March 2003.
23. R.P. Stanley, Hyperplane arrangements, parking functions and tree inversions, in "Mathematical Essays in Honor of Gian-Carlo Rota" (B.E. Sagan and R.P. Stanley, eds.), Progress in Math. 181 (1998), Birkhäuser, Boston, pp. 359-375. MR 99f:05006
24. R.A. Sulanke, Catalan path statistics having the Narayana distribution, Discrete Math. 180 (1998), 369-389. MR 99b:05004