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largest possible cardinality of a set

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February 25, 2006
vectorlinear algebramatrixcombinatorics

Problem Statement

Given is a prime number pp and natural nn such that p≥n≥3p \geq n \geq 3. Set AA is made of sequences of lenght nn with elements from the set {0,1,2,...,p−1}\{0,1,2,...,p-1\} and have the following property: For arbitrary two sequence (x1,...,xn)(x_1,...,x_n) and (y1,...,yn)(y_1,...,y_n) from the set AA there exist three different numbers k,l,mk,l,m such that: xk≠ykx_k \not = y_k, xl≠ylx_l \not = y_l, xm≠ymx_m \not = y_m. Find the largest possible cardinality of AA.
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