3 search hits

A survey of the higher StasheffTamari orders
(2012)

Jörg Rambau
Victor Reiner
 The Tamari lattice, thought as a poset on the set of triangulations of a convex polygon with n vertices, generalizes to the higher StasheffTamari orders on the set of triangulations of a cyclic ddimensional polytope having n vertices. This survey discusses what is known about these orders, and what one would like to know about them.

There are integral heptagons, no three points on a line, no four on a circle
(2007)

Tobias Kreisel
Sasch Kurz
 We give two configurations of seven points in the plane, no three points in a line, no four points on a circle with pairwise integral distances. This answers a famous question of Paul Erdös.

Convex hulls of polyominoes
(2007)

Sascha Kurz
 In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facettofacet connected system of $n$ unit hypercubes in $mathbb{R}^d$. For $d=2$ we enumerate the extremal polyominoes and determine the set of possible areas of the convex hull for each $n$.