On the Bounded Complex of an Affine Oriented Matroid

نویسنده

  • Xun Dong
چکیده

We prove that the bounded complex of an affine oriented matroid is pure and collapsible. We also generalize Zaslavsky’s Central Decomposition Theorem for hyperplane arrangements to affine oriented matroids.

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

The bounded complex of a uniform affine oriented matroid is a ball

Zaslavsky conjectures that the bounded complex of a simple hyperplane arrangement is homeomorphic to a ball. We prove this conjecture for the more general uniform affine oriented matroids.

متن کامل

On tope graphs of complexes of oriented matroids

We give two graph theoretical characterizations of tope graphs of (complexes of) oriented matroids. The first is in terms of excluded partial cube minors, the second is that all antipodal subgraphs are gated. A direct consequence is a third characterization in terms of zone graphs of tope graphs. Further corollaries include a characterization of topes of oriented matroids due to da Silva, anoth...

متن کامل

Antisymmetric flows in matroids

We present a seemingly new definition of flows and flow numbers for oriented matroids and prove that the flow number ΦL and the antisymmetric flow number ΦLas of an oriented matroid are bounded with its rank. In particular we show that if O is an oriented matroid of rank r then ΦL(O) ≤ r + 2 and ΦLas(O) ≤ 3b 9 2 rc+1. Furthermore, we introduce the notion of a semiflow and show that each oriente...

متن کامل

Balancing Covectors

Recently, Goddyn, Hochstättler and Hliněný proved that the oriented flow number introduced by Goddy, Tarsi and Zhang for an oriented matroid of rank r is bounded by 14r2 ln r. We improve this bound by showing that any oriented matroid without a coloop admits a reorientation such the imbalance of each covector is at most 3r − 1. In particular this yields a new upper bound for the oriented flow n...

متن کامل

Search for a “gravitoid” Theory

By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M-theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson-Davis. Also, by considering the oriented matroid theory...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • Discrete & Computational Geometry

دوره 35  شماره 

صفحات  -

تاریخ انتشار 2006