Lattice paths and determinants

  • Martin Aigner
  • Günter M. Ziegler


The essence of mathematics is proving theorems — and so, that is what mathematicians do: they prove theorems. But to tell the truth, what they really want to prove, once in their lifetime, is a Lemma, like the one by Fatou in analysis, the Lemma of Gauss in number theory, or the Burnside-Frobenius Lemma in combinatorics.


Bipartite Graph Acyclic Directed Graph Lattice Path Minimal Index Hook Length 
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  1. [1]
    I. M. Gessel & G. Viennot: Binomial determinants, paths, and hook leng, formulae, Advances in Math. 58 (1985), 300–321.MathSciNetzbMATHCrossRefGoogle Scholar
  2. [2]
    B. Lindstrőm: On the vector representation of induced matroids, Bullet London Math. Soc. 5 (1973), 85–90.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Martin Aigner
    • 1
  • Günter M. Ziegler
    • 2
  1. 1.Institut für Mathematik II (WE2)Freie Universität BerlinBerlinGermany
  2. 2.Institut für Mathematik, MA 6-2Technische Universität BerlinBerlinGermany

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