Small Forbidden Configurations III

نویسندگان

Richard P. Anstee

N. Kamoosi

چکیده

The present paper continues the work begun by Anstee, Ferguson, 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). 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 largest n, which would depend on m and F , so that such an A exists. ‘Small’ refers to the size of k and in this paper k = 2. For p ≤ q, we set Fpq to be the 2 × (p + q) matrix with p 1 0 ] ’s and q 0 1 ] ’s. We give new exact values: forb(m,F0,4) = b 5m 2 c + 2, forb(m,F1,4) = b 11m 4 c + 1, forb(m,F1,5) = b 15m 4 c + 1, forb(m,F2,4) = b 10m 3 − 4 3c and forb(m,F2,5) = 4m (For forb(m,F1,4), forb(m,F1,5) we obtain equality only for certain classes modulo 4). In addition we provide a surprising construction which shows forb(m,Fpq) ≥ p+q 2 + O(1) ) m.

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