메뉴 건너뛰기




Volumn 18, Issue 2, 2004, Pages 397-417

Noncrossing partitions for the group D n

Author keywords

Antichain; Catalan number; Garside structure; Narayana numbers; Noncrossing partition; Nonnesting partition; Reflection group; Root poset; Type D

Indexed keywords

ANTICHAIN; CATALAN NUMBER; GARSIDE STRUCTURES; NARAYANA NUMBERS; NONNCROSSINNG PARTITIONS; NONNESTING PARTITION; REFLECTION GROUPS; ROOT POSET; TYPE D;

EID: 18844445398     PISSN: 08954801     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0895480103432192     Document Type: Article
Times cited : (86)

References (28)
  • 1
    • 0012674905 scopus 로고    scopus 로고
    • On noncrossing and nonnesting partitions for classical reflection groups
    • Research Paper 42, (electronic)
    • C. A. ATHANASIADIS, On noncrossing and nonnesting partitions for classical reflection groups, Electron. J. Combin., 5 (1998), Research Paper 42, 16 pp. (electronic).
    • (1998) Electron. J. Combin. , vol.5
    • Athanasiadis, C.A.1
  • 2
    • 2642567076 scopus 로고    scopus 로고
    • Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes
    • C. A. ATHANASIADIS, Generalized Catalan numbers, Weyl groups and arrangements of hyperplanes, Bull. London Math. Soc., 36 (2004), pp. 294-302.
    • (2004) Bull. London Math. Soc. , vol.36 , pp. 294-302
    • Athanasiadis, C.A.1
  • 3
    • 12844277556 scopus 로고    scopus 로고
    • On a refinement of the generalized Catalan numbers for Weyl groups
    • C. A. ATHANASIADIS, On a refinement of the generalized Catalan numbers for Weyl groups, Trans. Amer. Math. Soc., 357 (2005), pp. 179-196.
    • (2005) Trans. Amer. Math. Soc. , vol.357 , pp. 179-196
    • Athanasiadis, C.A.1
  • 6
    • 0036698115 scopus 로고    scopus 로고
    • Springer theory in braid groups and the Birman-Ko-Lee monoid
    • D. BESSIS, F. DIGNE, AND J. MICHEL, Springer theory in braid groups and the Birman-Ko-Lee monoid, Pacific J. Math., 205 (2002), pp. 287-309.
    • (2002) Pacific J. Math. , vol.205 , pp. 287-309
    • Bessis, D.1    Digne, F.2    Michel, J.3
  • 7
    • 0002964353 scopus 로고    scopus 로고
    • Some properties of crossings and partitions
    • P. BIANE, Some properties of crossings and partitions, Discrete Math., 175 (1997), pp. 41-53.
    • (1997) Discrete Math. , vol.175 , pp. 41-53
    • Biane, P.1
  • 8
    • 0344183200 scopus 로고    scopus 로고
    • Parking functions of types a and B
    • Note 7, (electronic)
    • P. BIANE, Parking functions of types A and B, Electron. J. Combin., 9 (2002), Note 7, 5 pp. (electronic).
    • (2002) Electron. J. Combin. , vol.9
    • Biane, P.1
  • 10
    • 33646886315 scopus 로고
    • Shellable and cohen-macaulay partially ordered sets
    • A. BJÖRNER, Shellable and Cohen-Macaulay partially ordered sets, Trans. Amer. Math. Soc., 260 (1980), pp. 159-183.
    • (1980) Trans. Amer. Math. Soc. , vol.260 , pp. 159-183
    • Björner, A.1
  • 11
    • 0035880076 scopus 로고    scopus 로고
    • A partial order on the symmetric group and new K(π, 1)'s for the braid groups
    • T. BRADY, A partial order on the symmetric group and new K(π, 1)'s for the braid groups, Adv. Math., 161 (2001), pp. 20-40.
    • (2001) Adv. Math. , vol.161 , pp. 20-40
    • Brady, T.1
  • 12
    • 0036415374 scopus 로고    scopus 로고
    • K(π, 1)'s for Artin groups of finite type
    • Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000)
    • T. BRADY AND C. WATT, K(π, 1)'s for Artin groups of finite type, in Proceedings of the Conference on Geometric and Combinatorial Group Theory, Part I (Haifa, 2000), Geom. Dedicata, 94 (2002), pp. 225-250.
    • (2002) Geom. Dedicata , vol.94 , pp. 225-250
    • Brady, T.1    Watt, C.2
  • 13
    • 0000266671 scopus 로고
    • Chain enumeration and noncrossing partitions
    • P. H. EDELMAN, Chain enumeration and noncrossing partitions, Discrete Math., 31 (1980), pp. 171-180.
    • (1980) Discrete Math. , vol.31 , pp. 171-180
    • Edelman, P.H.1
  • 14
    • 0030584844 scopus 로고    scopus 로고
    • On posets and Hopf algebras
    • R. EHRENBORG, On posets and Hopf algebras, Adv. Math., 119 (1996), pp. 1-25.
    • (1996) Adv. Math. , vol.119 , pp. 1-25
    • Ehrenborg, R.1
  • 15
    • 0002532511 scopus 로고
    • Reflection groups and coxeter groups
    • Cambridge University Press, Cambridge, UK
    • J. E. HUMPHREYS, Reflection Groups and Coxeter Groups, Cambridge Studies in Advanced Mathematics 29, Cambridge University Press, Cambridge, UK, 1990.
    • (1990) Cambridge Studies in Advanced Mathematics , vol.29
    • Humphreys, J.E.1
  • 16
    • 0000513203 scopus 로고
    • Sur les partitions non-croisées d'un cycle
    • G. KREWERAS, Sur les partitions non-croisées d'un cycle, Discrete Math., 1 (1972), pp. 333-350.
    • (1972) Discrete Math. , vol.1 , pp. 333-350
    • Kreweras, G.1
  • 18
    • 0000153674 scopus 로고    scopus 로고
    • A "Fourier transform" for multiplicative functions on non-crossing partitions
    • A. NICA AND R. SPEICHER, A "Fourier transform" for multiplicative functions on non-crossing partitions, J. Algebraic Combin., 6 (1997), pp. 141-160.
    • (1997) J. Algebraic Combin. , vol.6 , pp. 141-160
    • Nica, A.1    Speicher, R.2
  • 19
    • 0038730345 scopus 로고    scopus 로고
    • Explicit presentations for the dual braid monoids
    • M. PlCANTlN, Explicit presentations for the dual braid monoids, C. R. Math. Acad. Sci. Paris, 334 (2002), pp. 843-848.
    • (2002) C. R. Math. Acad. Sci. Paris , vol.334 , pp. 843-848
    • Plcantln, M.1
  • 20
    • 0001135742 scopus 로고    scopus 로고
    • Non-crossing partitions for classical reflection groups
    • V. REINER, Non-crossing partitions for classical reflection groups, Discrete Math., 177 (1997), pp. 195-222.
    • (1997) Discrete Math. , vol.177 , pp. 195-222
    • Reiner, V.1
  • 21
    • 0000790354 scopus 로고    scopus 로고
    • Noncrossing partitions
    • R. SIMION, Noncrossing partitions, Discrete Math., 217 (2000), pp. 367-409.
    • (2000) Discrete Math. , vol.217 , pp. 367-409
    • Simion, R.1
  • 22
    • 0002207827 scopus 로고
    • On the structure of the lattice of non-crossing partitions
    • R. SIMION AND D. ULLMAN, On the structure of the lattice of non-crossing partitions, Discrete Math., 98 (1991), pp. 193-206.
    • (1991) Discrete Math. , vol.98 , pp. 193-206
    • Simion, R.1    Ullman, D.2
  • 23
    • 24344506697 scopus 로고    scopus 로고
    • B-stable ideals in the nilradical of a Borel subalgebra
    • to appear
    • E. SOMMERS, B-stable ideals in the nilradical of a Borel subalgebra, Canad. Math. Bull., to appear.
    • Canad. Math. Bull.
    • Sommers, E.1
  • 24
    • 0003652674 scopus 로고
    • Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA
    • R. P. STANLEY, Enumerative Combinatorics, Vol. 1, Wadsworth & Brooks/Cole Advanced Books & Software, Monterey, CA, 1986;
    • (1986) Enumerative Combinatorics , vol.1
    • Stanley, R.P.1
  • 25
    • 0003581940 scopus 로고    scopus 로고
    • second printing, Cambridge University Press, Cambridge, UK
    • second printing, Cambridge Studies in Advanced Mathematics 49, Cambridge University Press, Cambridge, UK, 1996.
    • (1996) Cambridge Studies in Advanced Mathematics , vol.49
  • 26
    • 0003279650 scopus 로고    scopus 로고
    • Enumerative combinatorics
    • Cambridge University Press, Cambridge, UK
    • R. P. STANLEY, Enumerative Combinatorics, Vol. 2, Cambridge Studies in Advanced Mathematics 62, Cambridge University Press, Cambridge, UK, 1999.
    • (1999) Cambridge Studies in Advanced Mathematics , vol.2-62
    • Stanley, R.P.1
  • 27
    • 0001783864 scopus 로고    scopus 로고
    • Flag-symmetric and locally rank-symmetric partially ordered sets
    • Research Paper 6, (electronic)
    • R. P. STANLEY, Flag-symmetric and locally rank-symmetric partially ordered sets, Electron. J. Combin., 3 (1996), Research Paper 6, 22 pp. (electronic).
    • (1996) Electron. J. Combin. , vol.3
    • Stanley, R.P.1
  • 28
    • 0347413370 scopus 로고    scopus 로고
    • Parking functions and noncrossing partitions
    • Research Paper 20, (electronic)
    • R. P. STANLEY, Parking functions and noncrossing partitions, Electron. J. Combin., 4 (1997), Research Paper 20, 14 pp. (electronic).
    • (1997) Electron. J. Combin. , vol.4
    • Stanley, R.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.