Motivated by the question of when the characteristic polynomial of a matroid factorizes, we study join-factorizations of broken circuit complexes and rooted complexes (a more general class of complexes). Such factorizations of complexes induce factorizations not only of characteristic polynomial but also of the Orlik-Solomon algebra of the matroid. The broken circuit complex of a matroid factor...

A certain unimodal conjecture in matroid theory states the number of rank-r matroids on a set of size n is unimodal in r and attains its maximum at r = bn/2c. We show that this conjecture holds up to r = 3 by constructing a map from a class of rank-2 matroids into the class of loopless rank-3 matroids. Similar inequalities are proven for the number of non-isomorphic loopless matroids, loopless ...

Given a matroid M with distinguished element e, a port oracle with respect to e reports whether or not a given subset contains a circuit that contains e. The rst main result of this paper is an algorithm for computing an e-based ear decomposition (that is, an ear decomposition every circuit of which contains element e) of a matroid using only a polynomial number of elementary operations and por...

Catlin and Jaeger proved that the cycle matroid of a 4-edge-connected graph has a spanning cycle. This result can not be generalized to regular matroids as there exist infinitely many connected cographic matroids, each of which contains a M(K5) minor and has arbitrarily large cogirth, that do not have spanning cycles. In this paper, we proved that if a connected regular matroid without aM(K5)-m...

Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is ...

Let M be a matroid on a set E and let w : E −→ G be a weight function, where G is a cyclic group. Assuming that w(E) satisfies the Pollard’s Condition (i.e. Every non-zero element of w(E)−w(E) generates G), we obtain a formulae for the number of distinct base weights. If |G| is a prime, our result coincides with a result Schrijver and Seymour. We also describe Equality cases in this formulae. I...

Constructing structures with other mathematical theories is an important research field of rough sets. As one mathematical theory on sets, matroids possess a sophisticated structure. This paper builds a bridge between rough sets and matroids and establishes the matroidal structure of rough sets. In order to understand intuitively the relationships between these two theories, we study this probl...

In this paper we further investigate the structure of the convex sets of an acyclic oriented matroid. This subject was first explored by Las Vergnas [6]. The main tool of our study is the theory of the anti-exchange closure [2]. We show that the convex closure of Las Vergnas satisfies the anti-exchange law in the case where the matroid is a geometry. From this we are able to detail the structur...

of the bachelor's thesis Abstract: Locally repairable codes (LRCs) are error correcting codes used in distributed data storage. A traditional approach is to look for codes which simultaneously maximize error tolerance and minimize storage space consumption. However, this tends to yield codes for which error correction requires an unrealistic amount of communication between storage nodes. LRCs s...