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The origin of these studies was the work of Pontryagin, Postnikov, and Norman Steenrod, who first defined the Pontryagin square, Postnikov square, and Steenrod square operations for singular cohomology, in the case of mod 2 coefficients.
The combinatorial aspect there arises as a formulation of the failure of a natural diagonal map, at cochain level.
The general theory of the Steenrod algebra of operations has been brought into close relation with that of the symmetric group.

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