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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.
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?
…
- 13.1k
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