MathDB
Construction problem

Source: Indonesia TSTST - Combinatoric

February 29, 2024
combinatoricsmaximizationIndonesiaIndonesia TST

Problem Statement

Given a sequence of integers A1,A2,⋯A99A_1,A_2,\cdots A_{99} such that for every sub-sequence that contains mm consecutive elements, there exist not more than max{m3,1}max\{ \frac{m}{3} ,1\} odd integers. Let S={(i,j) ∣i<j}S=\{ (i,j) \ | i<j \} such that AiA_i is even and AjA_j is odd. Find max{∣S∣}max\{ |S|\}.
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