What's the noun for parities? Here's the word you're looking for.
parity
(uncountable)Equality; comparability of strength or intensity.
(mathematics) A set with the property of having all of its elements belonging to one of two disjointsubsets, especially a set of integers split in subsets of even and odd elements.
(mathematics) The classification of an element of a set with parity into one of the two sets.
(physics) Symmetry of interactions under spatial inversion.
(game) In reversi, the last move within a given sector of the board.