Israel Journal of Mathematics

, Volume 71, Issue 3, pp 309–320 | Cite as

Rank of inclusion matrices and modular representation theory

  • Avital Frumkin
  • Arieh Yakir


We use results from the modular representation theory of the groupsS n and GL n (F q ) to determine the rank of inclusion matrices.


Representation Theory Symmetric Group Permutation Group Incidence Matrix Independent Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    P. Frankl,Intersection theorems and mod p rank of inclusion matrices, J. Comb. Theory, Ser. A54 (1990), 85–94.MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    D. H. Gottlieb,A certain class of incidence matrices, Proc. Am. Math. Soc.17 (1966), 1233–1237.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    R. L. Graham, S.-Y.R. Li and W.-C.W. Li,On the structure of t-designs, SIAM J. Alg. Disc. Methods1 (1980), 8–14.MATHMathSciNetGoogle Scholar
  4. 4.
    G. D. James,The representation theory of the symmetric groups, Lecture Notes in Math., Vol. 682, Springer-Verlag, Berlin, 1978.MATHGoogle Scholar
  5. 5.
    G. D. James,Representations of general linear groups, London Math. Soc. Lect. Note Ser., Vol. 94, Cambridge University Press, 1984.Google Scholar
  6. 6.
    W. M. Kantor,On incidence matrices of finite projective and affine spaces, Math. Z.124 (1972), 315–318.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    N. Linial and B. L. Rothschild,Incidence matrices of subsets — a rank formula, SIAM J. Alg. Disc. Methods2 (1981), 333–340.MATHMathSciNetGoogle Scholar
  8. 8.
    R. M. Wilson,A diagonal form for the incidence matrices of t-subsets vs. k-subsets, Eur. J. Combinatorics, to appear.Google Scholar
  9. 9.
    A. Yakir,The permutation representation of the general affine group on the set of affine subspaces, in preparation.Google Scholar

Copyright information

© Hebrew University 1990

Authors and Affiliations

  • Avital Frumkin
    • 1
  • Arieh Yakir
    • 1
  1. 1.Institute of MathematicsThe Hebrew University of JerusalemJerusalemIsrael

Personalised recommendations