Pattern Recognition on Oriented Matroids: Halfspaces, Convex Sets and Tope Committees

The principle of inclusion-exclusion is applied to subsets of maximal covectors contained in halfspaces of a simple oriented matroid and to convex subsets of its ground set for enumerating tope committees.

Mathematics Computer Science

Paper

References (11)

01Oriented MatroidsJürgen Richter-Gebert, Günter M. Ziegler2017 · Handbook of Discrete and Computational Geometry, 2nd Ed. · 608 citations

02MyastheniaGravis(MG) in a patient with Juvenile Idiopathic ArthritisChristiaan Scott, A. Kalla2011 · Pediatric Rheumatology Online Journal · 368 citations

03Pattern Recognition on Oriented Matroids: K*-Vectors and ReorientationsA. Matveev2010 · 2 citations In Library

04Pattern Recognition on Oriented Matroids: Three-Tope CommitteesA. Matveev2008 · 4 citations

05Pattern Recognition on Oriented Matroids: Layers of Tope CommitteesA. Matveev2006 · 8 citations

06Pattern Recognition on Oriented Matroids: The Existence of a Tope CommitteeA. Matveev2006 · 6 citations

07Relative blocking in posetsA. Matveev2004 · Journal of combinatorial optimization · 13 citations

08ALGEBRAIC COMBINATORICSAlexander Garver, T. McConville2013 · 1.1k citations

09Convex, Acyclic, and Free Sets of an Oriented MatroidPaul H. Edelman, V. Reiner, V. Welker2002 · Discrete & Computational Geometry · 17 citations

10Oriented matroidsJ. Folkman, J. Lawrence1978 · J. Comb. Theory B · 953 citations

11E-mail address: andrey.o.matveev@gmail

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