Eigensets and power products of a bimatroid

AbstractWe consider a bimatroid (linking system) which has a natural one-to-one corre-spondence between the row set and the column set. Such bimatroid can be regarded as a combinatorial counterpart of a matrix which is subject to similarity transformations. For such a bimatroid we can consider the power product, introduce the notion of an “eigenset,” which is a combinatorial analogue of an eigenvector, and define the “Jordan type;” in particular, the maximum size of an eigenset is characterized by the rank of the power products