Excluded permutation matrices and the Stanley?Wilf conjecture

A MARCUS
2004 Journal of combinatorial theory. Series A  
This paper examines the extremal problem of how many 1-entries an n n 0-1 matrix can have that avoids a certain fixed submatrix P: For any permutation matrix P we prove a linear bound, settling a conjecture of Zolta´n Fü redi and Pe´ter Hajnal (Discrete Math. 103(1992) 233). Due to the work of Martin Klazar (D. Krob, A.A. Mikhalev, A.V. Mikhalev (Eds.), Formal Power Series and Algebraics Combinatorics, Springer, Berlin, 2000, pp. 250-255), this also settles the conjecture of Stanley and Wilf on
more » ... the number of n-permutations avoiding a fixed permutation and a related conjecture of Alon and Friedgut (J. Combin Theory Ser A 89(2000) 133).
doi:10.1016/s0097-3165(04)00051-2 fatcat:dww2s2hmwbdszjc5st6xtzmts4