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Results tagged with co.combinatorics
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user 1784
Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.
21
votes
Euler-Maclaurin formula and Riemann-Roch
Euler-Maclaurin's formula transforms the integral $I=\int_a^b f(x)dx$ into the finite sum $S=\sum_a^b f(x)$, for two integers $a,b$. As Dmitri pointed out, in 1993 Khovanskii and Pukhlikov gave a mult …
- 13.1k
62
votes
7
answers
7k
views
Euler-Maclaurin formula and Riemann-Roch
Let $Df$ denote the derivative of a function $f(x)$ and $\bigtriangledown f=f(x)-f(x-1)$ be the discrete derivative. Using the Taylor series expansion for $f(x-1)$, we easily get $\bigtriangledown = …
- 13.1k
11
votes
Elliptic Curves over F_1?
As was mentioned by others, currently varieties over $\mathbb F_1$ look uncomfortably like toric varieties or something very close to that. But of course there is a way to think of an elliptic curve a …
- 13.1k
11
votes
Accepted
Detecting tilings by toric geometry
A related question (but not exactly the one you asked) is:
Can one tell if a convex polytope $P$ and its translations by $\mathbb Z^n$ tile $\mathbb R^n$? Which polytopes $P$ have this property?
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- 13.1k