Combinatorial Generation of Small Point Configurations and Hyperplane Arrangements
نویسندگان
چکیده
A recent progress on the complete enumeration of oriented matroids enables us to generate all combinatorial types of small point configurations and hyperplane arrangements in general dimension, including degenerate ones. This extends a number of former works which concentrated on the non-degenerate case and are usually limited to dimension 2 or 3. Our initial study on the complete list for small cases has shown its potential in resolving geometric conjectures.
منابع مشابه
Complete combinatorial generation of small point configurations and hyperplane arrangements
A recent progress on the complete enumeration of oriented matroids enables us to generate all combinatorial types of small point configurations and hyperplane arrangements in general dimension, including degenerate ones. This extends a number of former works which concentrated on the nondegenerate case and are usually limited to dimension 2 or 3. Our initial study on the complete list for small...
متن کاملCounting External Facets of Simple Hyperplane Arrangements
The number of external facets of a simple arrangement depends on its combinatorial type. A computation framework for counting the number of external facets is introduced and improved by exploiting the combinatorial structure of the set of sign vectors of the cells of the arrangement. 1 Background and introduction n hyperplanes in dimension d form a hyperplane arrangement. An hyperplane arrangem...
متن کاملDescent algebras, hyperplane arrangements, and shuffling cards. To appear
This note establishes a connection between Solomon’s descent algebras and the theory of hyperplane arrangements. It is shown that card-shuffling measures on Coxeter groups, originally defined in terms of descent algebras, have an elegant combinatorial description in terms of random walk on the chambers of hyperplane arrangements. As a corollary, a positivity conjecture of Fulman is proved.
متن کاملDescent Algebras, Hyperplane Arrangements, and Shuuing Cards
This note establishes a connection between Solomon's descent algebras and the theory of hyperplane arrangements. It is shown that card-shu ing measures on Coxeter groups, originally de ned in terms of descent algebras, have an elegant combinatorial description in terms of randomwalk on the chambers of hyperplane arrangements. As a corollary, a positivity conjecture of Fulman is proved. 2
متن کاملThe Catalan Threshold Arrangement
Hyperplane arrangements are very interesting combinatorial objects and many results can be found in the literature. For instance, several papers [1, 2, 6, 7] are concerned with the characteristic polynomials and the number of regions of a hyperplane arrangement. In his paper [9], Stanley reviewed various hyperplane arrangements raising interesting questions, one of which is related to the follo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003