Quaternary Bicycle Matroids and the Penrose Polynomial for Delta-Matroids

摘要: In contrast to matroids, vf-safe delta-matroids have three kinds of minors and are closed under the operations twist loop complementation. We show that representable over GF(4) with respect nontrivial automorphism form a subclass particular, quaternary matroids vf-safe. Using this result, we matroid bicycle space M is obtained from by using As consequence, independent chosen representation. This also leads to, e.g., an extension known parity-type characterization dimension, generalization tripartition Rosenstiehl Read [Ann. Disc. Math. (1978)], suitable dual notions bipartite Eulerian binary delta-matroids. Finally, generalize number results concerning Penrose polynomial general setting turns out recursive relation much like Tutte polynomial.