A generalization to bases common to r binary matroids of the weighted matrix-tree theorem in the case when the weights are Boolean
The author proves a matroid theorem that generalizes the weighted matrix- tree theorem for graphs. A consequence of this theorem is that if M and N are binary matroids of the same rank having the same ground set S, then M and N have an even number of common bases if and only if there is a subset P of S which has partitions both into circuits of M and into cocircuits of N. Several other results for graphs and digraphs are also deduced from the main theorem.
scientific article; zbMATH DE number 3875301