Small Forbidden Configurations IV: The 3 Rowed Case

The present paper continues the work begun by Anstee, Griggs and Sali on small forbidden configurations. We define a matrix to be simple if it is a (0,1)-matrix with no repeated columns. Let F be a k×l (0,1)-matrix (the forbidden configuration). Small refers to the size of k and in this paper k = 3. Assume A is an m×n simple matrix which has no submatrix which is a row and column permutation of F. We define forb(m,F) as the best possible upper bound on n, for such a matrix A, which depends on m and F. We complete the classification for all 3-rowed (0,1)-matrices of forb (m,F) as either Θ(m), Θ(m 2) or Θ(m 3) (with constants depending on F).

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Correspondence to Richard Anstee*.

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* Research is supported in part by NSERC.

† Research was done while the second author visited the University of British Columbia supported by NSERC of first author. Research was partially supported by Hungarian National Research Fund (OTKA) numbers T034702 and T037846.

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Anstee*, R., Sali†, A. Small Forbidden Configurations IV: The 3 Rowed Case. Combinatorica 25, 503–518 (2005).

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Mathematics Subject Classification (2000):

  • 05D05
  • 05C65
  • 05C35