3 search hits
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A survey of the higher Stasheff-Tamari orders
(2012)
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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 Stasheff-Tamari orders on the set of triangulations of a cyclic d-dimensional polytope having n vertices. This survey discusses what is known about these orders, and what one would like to know about them.
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There are integral heptagons, no three points on a line, no four on a circle
(2007)
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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.
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Convex hulls of polyominoes
(2007)
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Sascha Kurz
- In this article we prove a conjecture of Bezdek, Brass, and Harborth concerning the maximum volume of the convex hull of any facet-to-facet 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 $n$.
