# Tagged Questions

**3**

votes

**0**answers

103 views

### What is the combinatorial data classifying non-normal affine toric varieties?

Recall that a toric variety is a variety $V$ containing an open dense algebraic torus. Here an algebraic torus means a finite product of copies of the multiplicative group of the ground field (which I ...

**2**

votes

**0**answers

196 views

### Complete presentations for one-relator semigroups (100\$+100\$ question)

It is an open problem whether word problem for one-relator semigroups is decidable, but it is even unnknown if one-relator semigroups always admit finite complete presentations (i.e. a finite complete ...

**25**

votes

**3**answers

538 views

### What is the probability two random maps on n symbols commute?

It is well known that two randomly chosen permutations of $n$ symbols commute with probability $p_n/n!$ where $p_n$ is the number of partitions of $n$. This is a special case of the fact that in a ...

**2**

votes

**2**answers

286 views

### How many idempotent relations are there on an $n$-element set?

As far as I know, it is an open problem to give a formula counting transitive relations on an $n$-element set. Is it easier to count the idempotent relations, that is relations that are both ...

**24**

votes

**5**answers

1k views

### How many binary operations are associative?

Let $X$ be a finite set of $n$ elements, and consider a binary operation $\odot: X \times X \rightarrow X$. There are $n^{n^2}$ such binary operations, as the $n \times n$ table entries can each
be ...

**6**

votes

**2**answers

299 views

### Wants: Polynomial Time Algorithm for Decomposing a Multiset of Rationals into Two Additive Subsets.

First, allow me to say that this problem was posed to me by a professor in the department. It is related to his research in a way that I do not know. However, since I couldn't come up with anything ...