In any two-step puzzle, the numbers of 7-labels and soft crossings are determined solely by the boundary 012 strings via the closed formulas in Corollary 2.6.
Binomial determinants, paths, and hook length formulae
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Enumeration of crossings in two-step puzzles
In any two-step puzzle, the numbers of 7-labels and soft crossings are determined solely by the boundary 012 strings via the closed formulas in Corollary 2.6.