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. ...

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8
votes
0answers
156 views
+100

How to estimate $Pr[vr_i=ur_i]$ in the presence of rotations

Suppose we want to compute the probability that for two different random vectors (with elements that are $0$ or $1$), denoted by $v$ and $u$, multiplying them with the rotations of a random vector $r$ ...
2
votes
0answers
99 views
+100

Expected frequency of most frequent die roll

Suppose we have an fair $m$-sided die, and we roll it $n$ times. What is the expected frequency $E(n, m)$ of the most frequently rolled face? If we fix $n$ we can calculate $E(n,m)$ like so. Let ...
2
votes
0answers
44 views
+50

Decomposing the Complete Graph into Forests

Which spanning forests can we partition the complete graph $K_n$ into? I am primarily interested in partitions into one fixed isomorphism class of forest. I'm also assuming whatever divisibility ...