Cyclic polytopes, oriented matroids and intersections of quadrics

2016 ◽  
Vol 23 (1) ◽  
pp. 87-118 ◽  
Author(s):  
Vinicio Gómez-Gutiérrez
Keyword(s):  
Oriented Matroids ◽  
Cyclic Polytopes

scholarly journals Cyclic Polytopes and Oriented Matroids

2000 ◽  
Vol 21 (1) ◽  
pp. 49-64 ◽  
Author(s):  
Raul Cordovil ◽  
Pierre Duchet
Keyword(s):  
Oriented Matroids ◽  
Cyclic Polytopes

scholarly journals Large convex sets in oriented matroids

1988 ◽  
Vol 45 (3) ◽  
pp. 293-304 ◽  
Author(s):  
J.Richard Buchi ◽  
William E Fenton
Keyword(s):  
Convex Sets ◽  
Oriented Matroids

scholarly journals EIGENVALUES OF A RANDOM WALK ON ORIENTED MATROIDS

2006 ◽  
Vol 43 (1) ◽  
pp. 17-25
Author(s):  
Seung-Ho Ahn ◽  
Shin-Ok Bang
Keyword(s):  
Random Walk ◽  
Oriented Matroids

scholarly journals NORMAL CYCLIC POLYTOPES AND CYCLIC POLYTOPES THAT ARE NOT VERY AMPLE

2013 ◽  
Vol 96 (1) ◽  
pp. 61-77 ◽  
Author(s):  
TAKAYUKI HIBI ◽  
AKIHIRO HIGASHITANI ◽  
LUKAS KATTHÄN ◽  
RYOTA OKAZAKI
Keyword(s):  
Cyclic Polytope ◽  
Cyclic Polytopes ◽  
Positive Integers

AbstractLet $d$ and $n$ be positive integers such that $n\geq d+ 1$ and ${\tau }_{1} , \ldots , {\tau }_{n} $ integers such that ${\tau }_{1} \lt \cdots \lt {\tau }_{n} $. Let ${C}_{d} ({\tau }_{1} , \ldots , {\tau }_{n} )\subset { \mathbb{R} }^{d} $ denote the cyclic polytope of dimension $d$ with $n$ vertices $({\tau }_{1} , { \tau }_{1}^{2} , \ldots , { \tau }_{1}^{d} ), \ldots , ({\tau }_{n} , { \tau }_{n}^{2} , \ldots , { \tau }_{n}^{d} )$. We are interested in finding the smallest integer ${\gamma }_{d} $ such that if ${\tau }_{i+ 1} - {\tau }_{i} \geq {\gamma }_{d} $ for $1\leq i\lt n$, then ${C}_{d} ({\tau }_{1} , \ldots , {\tau }_{n} )$ is normal. One of the known results is ${\gamma }_{d} \leq d(d+ 1)$. In the present paper a new inequality ${\gamma }_{d} \leq {d}^{2} - 1$ is proved. Moreover, it is shown that if $d\geq 4$ with ${\tau }_{3} - {\tau }_{2} = 1$, then ${C}_{d} ({\tau }_{1} , \ldots , {\tau }_{n} )$ is not very ample.

scholarly journals The Varchenko determinant for oriented matroids

2019 ◽  
Vol 293 (3-4) ◽  
pp. 1415-1430 ◽  
Author(s):  
Winfried Hochstättler ◽  
Volkmar Welker
Keyword(s):  
Oriented Matroids
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