Complementation, local complementation, and switching in binary matroids
نویسندگان
چکیده
منابع مشابه
Binary Symmetric Matrix Inversion Through Local Complementation
We consider the Schur complement operation for symmetric matrices over GF(2), which we identify with graphs through the adjacency matrix representation. It is known that Schur complementation for such a matrix (i.e., for a graph) can be decomposed into a sequence of two types of elementary Schur complement operations: (1) local complementation on a looped vertex followed by deletion of that ver...
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Orbits of graphs under the operation edge local complementation (ELC) are defined. We show that the ELC orbit of a bipartite graph corresponds to the equivalence class of a binary linear code. The information sets and the minimum distance of a code can be derived from the corresponding ELC orbit. By extending earlier results on local complementation (LC) orbits, we classify the ELC orbits of al...
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This entry provides a verified implementation of rank-based Büchi Complementation [1]. The verification is done in three steps: 1. Definition of odd rankings and proof that an automaton rejects a word iff there exists an odd ranking for it. 2. Definition of the complement automaton and proof that it accepts exactly those words for which there is an odd ranking. 3. Verified implementation of the...
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ژورنال
عنوان ژورنال: Advances in Applied Mathematics
سال: 2021
ISSN: 0196-8858
DOI: 10.1016/j.aam.2020.102041