A note on the characteristic rank and related numbers


This note quantifies, via a sharp inequality, an interplay between

  1. (a)

    the characteristic rank of a vector bundle over a topological space X

  2. (b)

    the ℤ2-Betti numbers of X, and

  3. (c)

    sums of the numbers of certain partitions of integers.

In a particular context, (c) is transformed into a sum of the readily calculable Betti numbers of the real Grassmann manifolds.

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Corresponding author

Correspondence to Ľudovít Balko.

Additional information

Dedicated to Professor Masaharu Morimoto on the occasion of his 60th birthday

Part of this research was carried out while J. Korbaš was a member of the research teams 1/0330/13 and 2/0029/13 supported in part by the grant agency VEGA (Slovakia).

Communicated by Anatolij Dvurečenskij

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Balko, Ľ., Korbaš, J. A note on the characteristic rank and related numbers. Math. Slovaca 64, 1541–1544 (2014). https://doi.org/10.2478/s12175-014-0290-y

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2010 Mathematics Subject Classification

  • Primary 57R20
  • Secondary 05A17


  • Stiefel-Whitney class
  • characteristic rank
  • Betti number
  • partitions of integers
  • Grassmann manifold