2015/03/12 by Emanuele Delucchi, Delucchi, Emanuele, Tim Lindemann +1
Computer Science · Engineering · #Coding theory and cryptography #graph theory and CDMA systems #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.1503.03795
This note contributes to the structure theory of abstract rigidity matroids in general dimension. In the spirit of classical matroid theory, we prove several cryptomorphic characterizations of abstract rigidity matroids (in terms of circuits, cocircuits, bases, hyperplanes). Moreover, the study of hyperplanes in abstract rigidity matroids leads us to state (and support with significant evidence) a conjecture about characterizing the class of abstract rigidity matroids by means of certain "prescribed substructures". We then prove a recursive version of this conjecture.