Pinning–the very start, cnt. 3 (Certain 2-colorings)

Given integers $A\ B\ C\ D$ , we can easily and always uniquely recover integers $0 \le a < b < c < d < n$ such that

$A=\sigma(T_a)\qquad B=\sigma(T_b)\qquad C=\sigma(T_c)\qquad D=\sigma(T_d)$

It is enough to define:

$a:=\tau-A,\qquad b:=\tau-B,\qquad c:=\tau-C,\qquad d:=\tau-D$

where $\tau$ is defined below, and the existence is subjected to the conditions:

$\tau := \frac{A + B + C + D}3$ is an integer

$3 \le D < C < B < A \le 3\cdot(n-2)$

$B+C+D \ge 2\cdot A$

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Pinning–the very start, cnt. 3 (Certain 2-colorings)

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