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straight permutation

Source: created by Valentin Vornicu - Romanian TST 2003, problem 17

February 10, 2004
inequalitiessymmetrycombinatorics proposedcombinatorics

Problem Statement

A permutation σ:{1,2,…,n}→{1,2,…,n}\sigma: \{1,2,\ldots,n\}\to\{1,2,\ldots,n\} is called straight if and only if for each integer kk, 1≤k≤n−11\leq k\leq n-1 the following inequality is fulfilled ∣σ(k)−σ(k+1)∣≤2. |\sigma(k)-\sigma(k+1)|\leq 2. Find the smallest positive integer nn for which there exist at least 2003 straight permutations. Valentin Vornicu
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