# 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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### Minimum sum between permutations of elements in a matrix

So, for the purposes of creating a heuristic for a Sokoban AI, I have to solve the following problem (if you're curious, the elements of the matrix each represent taxicab distances from boxes to ...
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### Parity of the output of a polynomial

$n \epsilon Z+$ For $n=1,2,3...$ $f(n)=(1/2)(n^2-n)$ produces an output of 2 odd integers followed by 2 even integers, $(2O2E)$ $g(n)=(1/6)(-n^3+6n^2+1)$ produces an output of 3 odd integers ...
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### Number of triangles a point lies in on a plane

On a plane , there are $2n+1$ points where no three points are co-linear. Show that for any point $P$ which is one of the points, the number of triangles the interior of which $P$ lies in is always ...
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### How to find generator matrix and parity check matrix?

The $[n, n − 1, 2]$-parity check code has messages consisting of binary strings of length $n − 1$. Messages are encoded by adding an extra symbol which is the sum (mod 2) of the previous symbols. I ...
57 views

### Assigning to every odd number a triangular number. Does the converse hold?

Context: A triangular number is a number of the form $n(n+1)/2$ where $n\in \mathbb N$. Question: After application of two theorems in my textbook (the first one being that "a number $n$ is ...
Hi I'm studying quantum mechanics with Stephen Gasiorowicz's book. It says for the $n=2$ states of the hydrogen atom, the $l=0$ state has even parity and the $l=1$ state has odd parity. As far as I ...