Non-crossing partitions for classical reflection groups

Discrete Mathematics - Tập 177 Số 1-3 - Trang 195-222 - 1997
Victor Reiner1
1School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA;

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Tài liệu tham khảo

Athanasiadis, 1996

Björner, 1980, Shellable and Cohen-Macaulay partially ordered sets, Trans. AMS, 260, 159, 10.2307/1999881

Billey, 1993, Some combinatorial properties of Schubert polynomials, J. Algebraic Combin., 2, 345, 10.1023/A:1022419800503

Blass, 1995

Bonin, 1993, Some q-analogues of the Schröder numbers arising from combinatorial statistics on lattice paths, J. Statist. Plann. Inference, 34, 35, 10.1016/0378-3758(93)90032-2

Comtet, 1974

Doubilet, 1975, The idea of a generating function, 83

Edelman, 1980, Chain enumeration and non-crossing partitions, Discrete Math., 31, 171, 10.1016/0012-365X(80)90033-3

Edelman, 1996, Free arrangements and rhombic tilings, Discrete Comput. Geom., 15, 307, 10.1007/BF02711498

Edelman, 1994, Chains in the lattice of non-crossing partitions, Discrete Math., 126, 107, 10.1016/0012-365X(94)90257-7

Fan, 1996, A Hecke algebra quotient and some combinatorial applications, J. Algebraic Combin., 5, 175, 10.1023/A:1022443327568

Fomin, 1993

S.V. Fomin and X.G. Viennot, Combinatorial applications of the nil-Temperley-Lieb algebra, in preparation.

Garsia, 1980, Combinatorial methods in the theory of Cohen-Macaulay rings, Adv. Math., 38, 229, 10.1016/0001-8708(80)90006-7

Hanlon, 1993

Humphreys, 1990, Reflection Groups and Coxeter Groups, vol. 29

Józefiak, 1993, Basic derivations for subarrangements of Coxeter arrangements, J. Algebraic Combin., 2, 291, 10.1023/A:1022455716471

Kreweras, 1972, Sur les partitions non-croisées d'un cycle, Discrete Math., 1, 333, 10.1016/0012-365X(72)90041-6

Montenegro, 1993

Nica, 1994

A. Postnikov, personal communication, 1996.

Rainville, 1960

Sagan, 1987, Shifted tableaux, Schur Q-functions and a conjecture of R. Stanley, J. Combin. Theory Ser. A, 45, 62, 10.1016/0097-3165(87)90047-1

Shephard, 1954, Finite unitary reflection groups, Canad. J. Math., 6, 274, 10.4153/CJM-1954-028-3

Simion, 1994, Combinatorial statistics on non-crossing partitions, J. Combin. Theory Ser. A, 66, 270, 10.1016/0097-3165(94)90066-3

Simion, 1996, Octabasic Laguerre polynomials and permutation statistics, J. Comput. Appl. Math., 68, 297, 10.1016/0377-0427(95)00250-2

Simion, 1991, On the structure of the lattice of non-crossing partitions, Discrete Math., 98, 193, 10.1016/0012-365X(91)90376-D

Stanley, 1986, vol. I

Wachs, 1991, p, q-Stirling numbers and set partition statistics, J. Combin. Theory Ser. A, 56, 27, 10.1016/0097-3165(91)90020-H

White, 1994, Interpolating set partition statistics, J. Combin. Theory Ser. A, 68, 262, 10.1016/0097-3165(94)90107-4