manuscripta mathematica

, Volume 63, Issue 2, pp 129–155 | Cite as

Enumeration of lattice paths and generating functions for skew plane partitions

  • Christian Krattenthaler


n-dimensional lattice paths not touching the hyperplanesXiXi+1=−1,i=1,2,...,n, are counted by four different statistics, one of which is MacMahon's major index. By a reflection-like proof, heavily relying on Zeilberger's (Discrete Math. 44(1983), 325–326) solution of then-candidate ballot problem, determinantal expressions are obtained. As corollaries the generating functions for skew plane partitions, column-strict skew plane partitions, reverse skew plane plane partitions and column-strict reverse skew plane partitions, respectively, are evaluated, thus establishing partly new results, partly new proofs for known theorems in the theory of plane partitions.


Number Theory Algebraic Geometry Topological Group Discrete Math Lattice Path 
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Copyright information

© Springer-Verlag 1989

Authors and Affiliations

  • Christian Krattenthaler
    • 1
  1. 1.Institut für MathematikUniversität WienViennaAustria

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