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Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

4 votes

Equation in the conjugacy class of a free group

I don't think so. This boils down to finding a retraction from the group $\langle a,b,c,d,q,r,t\rangle/\langle\langle tQabRcdT=QbaRdc\rangle\rangle$ to the subgroup $\langle a,b,c,d\rangle$. The White …
seldom seen's user avatar
10 votes
2 answers
1k views

How many functions are there from a set to itself, up to isomorphism?

What is known about the (asymptotic?) behaviour of the number of equivalence classes of functions $n\to n$, where two functions are considered equivalent if they differ by a permutation of $n$, i.e., …