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A Combinatorial Identity Arising from Symplectic Geometry 被引量：1

A Combinatorial Identity Arising from Symplectic Geometry
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摘要 In this note, we give a generalization of the famous combinational identity （-1）^nn! = Σk=1^n （nk）（-1）^kk^n arising from symplectic geometry. In this note, we give a generalization of the famous combinational identity （-1）^nn! = Σk=1^n （nk）（-1）^kk^n arising from symplectic geometry.
作者 Hao DING
机构地区 School of Mathematical Sciences
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2009年第9期1497-1506,共10页 数学学报（英文版）
关键词 Duistermaat-Heckman theorem Hamiltonian S^1 action Grassmann manifold WEIGHT Duistermaat-Heckman theorem, Hamiltonian S^1 action, Grassmann manifold, weight
分类号 O157.4 [理学—基础数学] TP18 [自动化与计算机技术—控制理论与控制工程]
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参考文献8

  • 1Boole, G.: Calculus of Finite Differences, J. F. Moulton, ed., fourth edition, Chelsea Publishing Company, New York, 1970.
  • 2McDuff, D., Salamon, D.: Introduction to Symplectic Topology, second edition, Oxford University Press, Oxford, 1998.
  • 3Polterovich, L.: The Geometry of the Group of Symplectic Diffeomorphisms, Lectures in Mathematics, ETH, Birkhauser, Basel, 2001.
  • 4Duistermaat, J. J., Heckman, G. J.: On the variation in the cohomology of the symplectic form of the reduced phase space, Inventiones Mathematicae, 69, 259-268 (1982), Addendum in loc. cit., 72, 153-158 (1983).
  • 5Lu, G. C.: Gromov-Witten invariants and pseudo symplectic capacities. Israel Journal of Mathematics, 156, 1-63 (2006).
  • 6Lu, Q. K.: The heat kernels of noncompact symmetric spaces, Analysis and Geometry on Complex Homogeneous Domains, Progress in Mathematics, 185, Birkhauser, Basel, 2000.
  • 7Konechny, A., Rajeev, S. G., Turgut, O. T.: Classical Mechanics on Crassmannian and Disc. In: Geometry, Integrablity and Quantization II, Ivailo M. Mladenov and Gregory L. Naber, Eds., Coral Press, Sofia, 2001.
  • 8Lu, Q. K.: Classical Manifolds and Classical Domains, Shanghai Scientific and Technical Publishers, Shanghai, 1963, pp. 349-369 (in Chinese).

引证文献1

Acta Mathematica Sinica,English Series
2009年 第9期

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