# Questions tagged [parity]

This tag is for questions relating to "Parity", a mathematical term that describes the property of an integer's inclusion in one of two categories: even or odd.

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### How are there $2^n$ $n$-variable parity functions?

Source: https://www.cs.cmu.edu/~odonnell/boolean-analysis/lecture2.pdf Context: Linearity testing of boolean functions is being discussed, and they just introduced parity functions which I didn't know ...
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### What is the description of pseudo-quantities on a general manifold?

When talking about physics (on $\mathbb{R}^3$), one tends to call pseudovectors $+$-parity objects, since they transform into themselves under the parity transformation $P: (x,y,z) \mapsto (-x,-y,-z)$....
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### Formal expression for parity of three integers

During an X-Ray Crystal Diffraction course, we ended up with this sum : $$(-1)^{h+k} + (-1)^{k+l} + (-1)^{h+l} + 1$$ The condition of extinction for the diffraction is that the sum must be equal to 0 :...
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### On the number of ways to get a sum with given parity

Fix some integers $a_1,\dots,a_n\geq 0$. Denote by $E$ and $O$ the number of ways to choose $(x_1,\dots,x_n)$ so that $0\leq x_i\leq 2a_i$ and such that $\sum_{i=1}^n x_i$ is even and odd, ...
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