## Top new questions this week:

### The coupon collector's earworm

I thank Nicolas Dupont for the following question (and for permission to disseminate it further): I have a playlist with, say, $N$ pieces of music. While using the shuffle option (each such ...

reference-request co.combinatorics asymptotics
 asked by Noam D. Elkies 27 votes
 answered by Kevin P. Costello 11 votes

### Why should we care about "higher infinities" outside of set theory?

Let's say you are a prospective mathematician with some addled ideas about cardinality. If you assumed that the natural numbers were finite, you'd quickly vanish in a puff of logic. :) If you ...

set-theory soft-question
 answered by Joel David Hamkins 21 votes

### Which algebraic relations are possible between algebraic conjugates?

For which non-constant rational functions $f(x)$ in $\mathbb{Q}(x)$ is there $\alpha$, algebraic over $\mathbb{Q}$, such that $\alpha$ and $f(\alpha) \neq \alpha$ are algebraic conjugates? More ...

nt.number-theory polynomials

### A Linear Order from AP Calculus

In teaching my calculus students about limits and function domination, we ran into the class of functions $$\Theta=\{x^\alpha (\ln{x})^\beta\}_{(\alpha,\beta)\in\mathbb{R}^2}$$ Suppose we say that ...

co.combinatorics ct.category-theory real-analysis order-theory linear-orders

### Brouwer's theorem for the Cauchy reals

Brouwer famously proved, using principles motivated by intuitionistic choice sequences, that every function $\mathbb{R}\to \mathbb{R}$ is continuous. In Sheaves in geometry and logic (section VI.9), ...

ct.category-theory topos-theory constructive-mathematics sheaves

### Which sequential colimits commute with pullbacks in the category of topological spaces?

This question was asked on math.stackexchange.com without a reaction. Given diagrams of topological spaces $$X_0\rightarrow X_1\rightarrow\ldots$$ $$Y_0\rightarrow Y_1\rightarrow\ldots$$ ...

at.algebraic-topology ct.category-theory gn.general-topology

### How big is the lattice of all functions?

Define the lattice $(\mathcal{L},\prec)$ as the set of all function $f:\mathbb{N}\rightarrow\mathbb{N}$ satisfying $f(n)\leq f(n+1)\leq f(n)+1$, where two functions are considered equal if they differ ...

reference-request lattice-theory
 answered by Dominic van der Zypen 4 votes

## Greatest hits from previous weeks:

### Good programs for drawing graphs ( directed weighted graphs )

Does anyone know of a good program for drawing directed weighted graphs?

graph-theory software

### Video lectures of mathematics courses available online for free

It can be difficult to learn mathematics on your own from textbooks, and I often wish universities videotaped their mathematics courses and distributed them for free online. Fortunately, some ...

ho.history-overview mathematics-education soft-question big-list

## Can you answer these?

### Detecting torsion-classified bundles by differential invariants

The following is based on a loose understanding of the nuts and bolts that go into Chern-Simons theory, so bear with any vagueness on my part. Suppose I have a principal $G$-bundle $P\to M$ and I ...

dg.differential-geometry principal-bundles

### Indecomposable representations of a wreath product

If $G$ is a finite group, we know the irreducible representations of $G ≀ S_n$ (over $\mathbb Q$) are classified by partitions of $n$ 'decorated' by an irrep of $G$. I'm wondering to what extent the ...

gr.group-theory rt.representation-theory
We have the following theorem: Let $X$ be a projective scheme over an algebraically closed field $k$, and $Y \subset X$ a closed subscheme with Hilbert polynomial $P$. ThenT_{[Y]}\text{Hilb}_P (X) ...