# All Questions

100,960 questions
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### Parity, Balls and Boxes

Start with a distribution $\mu$ on [n], and drop m balls into these n+1 slots independently and according to the distribution &mu. That is, we have iid random variables x 1 through x m ...
764 views

### What is the geometric meaning of reconstruction of quantum group via Ringel Hall algebra

If I remembered correctly. There are some work done by C.M.Ringel,he defined so called Ringel-Hall algebra on abelian category and then show that Ringel-hall algebra is isomorphic to positive part of ...
2k views

### Lax Functors and Equivalence of Bicategories?

Lax functors of bicategories were introduced at the very inception of bicategories, and I'm trying to get a better feel for them. They are the same as ordinary 2-functors, but you only require the ...
2k views

### How do we study the theory of reductive groups? [closed]

I am interested in the theory of reductive groups which is useful in the theory of automorphic forms. But the trouble boring me so long time is that I don't know the appropriate material for beginners ...
12k views

### Why does the Gamma-function complete the Riemann Zeta function?

Defining $$\xi(s) := \pi^{-s/2}\ \Gamma\left(\frac{s}{2}\right)\ \zeta(s)$$ yields $\xi(s) = \xi(1 - s)$ (where $\zeta$ is the Riemann Zeta function). Is there any conceptual explanation - or ...
2k views

### Trace map attached to a finite homomorphism of noetherian rings

Let $f:A\rightarrow B$ be a homomorphism of noetherian rings which makes $B$ into a finite $A$-module. Under what conditions on $f$, $A$, $B$ can one associate to this map a canonical "trace map" \...
4k views

### Generalizations of Planar Graphs

This is a follow up to Harrison's question: why planar graphs are so exceptional. I would like to ask about (and collect answers to) various notions, in graph theory and beyond graph theory (topology; ...
2k views

### Break Polyhedron into Tetrahedron

Given a polyhedron consists of a list of vertices (v), a list of edges (e), and a list of surfaces connecting those edges (...
589 views

### Decomposition of Hölder continuous functions

Let $\alpha\in(0,1)$ and $\eta\in\Lambda_0^\alpha(\mathbb{R})$ be a compactly supported Hölder continuous function of order $\alpha$. I would like to show that, for any $n\in\mathbb{N}$, it is ...
713 views

### Tropicalizing the learning

Could someone tell me if it is possible to do tropical geometry with NO knowledge(or with very few) of algebraic geometry (a la Hartshorne)? By "do tropical geometry" I mean, to understand the ...
3k views

### Twin Prime Conjecture Reference

I'm looking for a reference which has the first statement of the twin prime conjecture. According to wikipedia, nova, and several other quasi-reputable resources it is Euclid who first stated it, but ...