# Questions tagged [lattice-polytopes]

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7 questions
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### Problem with the vertices of a convex quadrilateral on integer lattice

I made the following observation and I am wondering if it is always true. Let $x_1$, $x_2$, $x_3$ and $x_4$ be four positive integer points in the plane ($x_i\in\mathbb{Z^2_{\geq 0}}$) forming a ...
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### An Ehrhart positivity question related to Schur polynomials

Consider the Schur polynomial $s_\lambda(x_1,\dotsc,x_k)$. It is easy to see from the hook-content formula for counting the number of semi-standard tableaux, that the function  n \to s_{n \lambda}(1,...
215 views

### Minimum weight triangulation of lattice points in a circle

Let $r$ be a natural number, and consider the $\mathbb{Z}^2$ lattice points $S$ inside or on the circle $C$ of radius $r$ centered on the origin. Let $P$ be the convex hull of $S$; so $P$ is inscribed ...
### Does Barvinok's algorithm count modulo $q$ in $O(polylog (q))$ word size?
Let $Ax\leq b$ be a polyhedron in $n$-dimensions and $m$ constraints and $q>1$ be an integer. The number of points in the polyhedron could be exponential in $n$ and $m$ while $q\ll nm$ could be ...