Abstract

Let $\mathcal{𝒜}(n,k)$ denote the collection of all $n^k$ integer sequences $(a_1,a_2,\dots <!--FUNCTION\; APPLICATION-->,a_k)$, $1\le a_i\le n$. Let $m(n,k)$ be the maximum of $\left|\mathcal{ℱ}\right|$, $\mathcal{ℱ}\subset \mathcal{𝒜}(n,k)$ and no two sequences in $\mathcal{ℱ}$ coincide in exactly one coordinate. The main results are $m(n,k)=n^{k-2}$ for $k\ge 6$ and $n\ge n_0(k)$, $m(n,5)=(1+o(1))n^3$ and $m(n,4)=1+2{(n-1)}^2$ for $n\ge 3$. The integer sequence version of the Deza–Erdős–Frankl theorem is established as well.

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Mathematical Subject Classification

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