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PAMO 2017 Shortlst: Sum of maxima of adjacent pairs in permutation

Source: 2017 Pan-African Shortlist - I4

May 5, 2019
combinatoricsInequalitymaximum valueminimum valuepermutations

Problem Statement

Find the maximum and minimum of the expression max⁡(a1,a2)+max⁡(a2,a3),+⋯+max⁡(an−1,an)+max⁡(an,a1), \max(a_1, a_2) + \max(a_2, a_3), + \dots + \max(a_{n-1}, a_n) + \max(a_n, a_1), where (a1,a2,…,an)(a_1, a_2, \dots, a_n) runs over the set of permutations of (1,2,…,n)(1, 2, \dots, n).
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