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Young diagrams are fundamental combinatorial objects in representation theoryand algebraic geometry. Many constructions that rely on these objects depend onvariations of a straightening process that expresses a filling of a Youngdiagram as a sum of semistandard tableaux subject to certain relations. Thispaper solves the long standing open problem of giving a non-iterative formulafor straightening a filling. We apply our formula to give a completegeneralization of a theorem of Gonciulea and Lakshmibai.

A non-iterative formula for straightening fillings of Young diagrams