Tarotoast’s Stuff

Given permutations π and σ, a breakpoint between π and σ is defined as a pair of adjacent elements π_i and π_i+1 in π that are separated in σ. For example, if π = 143256 and σ = 123465, then π₁ = 1 and π₂= 4 in π form a breakpoint between π and σ since 1 and 4 are separated in σ. The number of breakpoints between π=01432567 and σ=01234567 is three (14, 25 and 67), while the number of breakpoints between σ and π is also three (12, 46 and 57).

Prove that the number of breakpoints between π and σ equals the number of breakpoints between σ and π.

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