This tag is for basic questions about the study of finite or countable discrete structures — specifically how to count or enumerate elements in a set (perhaps of all possibilities) or any subset. It includes questions on permutations, combinations, bijective proofs, and generating functions. ...
Consider a graph whose nodes are the integer partitions of $n$, connected by an edge if you can get from one partition to the other by ‘sliding one square of its Young diagram’ – that is, if one ...
Question: There are $n$ students sitting at a round table. You collect all $ n $ name tags and give them back arbitrarily. Each student gets one of the $n$ name tags. Now the $n$ students repeat ...
So I'm working on a problem where I get to a point where I have to count the number of solutions to an equation or at least find a decent upper bound to be used in an estimate I need later. The ...