We study the cycles generated by the chip firing game associated with n-cube orientations. We consider a particular class of partitions of vertices of n-cubes called left cyclic partitions that induce parallel periodic evolutions. Using this combinatorical model, we show that cycles generated by parallel evolutions are of even lengths from 2 to 2 on Hn (n ≥ 1), and of odd lengths different from...

Several applications require to estimate the power production of photovoltaic (PV) systems under partial shading conditions. For example, dynamic reconfiguration array connections is needed maximize conditions, which requires estimating generated by PV in several possible configurations. Therefore, a fast and accurate modeling technique perform those calculations practical times with low estima...

The family of 2-level matroids, that is, matroids whose base polytope is 2-level, has been recently studied and characterized by means of combinatorial properties. 2-level matroids generalize series-parallel graphs, which have been already successfully analyzed from the enumerative perspective. We bring to light some structural properties of 2-level matroids and exploit them for enumerative pur...

We show that a set of uniformly width-bounded infinite seriesparallel pomsets is ω-series-rational iff it is axiomatizable in monadic second order logic iff it is ω-recognizable. This extends recent work by Lodaya and Weil on sets of finite series-parallel pomsets in two aspects: It relates their notion of series-rationality to logical concepts, and it generalizes the equivalence of recognizabi...

We give a new characterization of series-parallel graphs which implies that the maximum integer multiflow is equal to the minimum capacity multicut if G + H is series-parallel, where G + H denotes the union of the support graph G and the demand graph H . We investigate the difference between a result of the type ‘‘the cut-condition is sufficient for the existence of a multiflow in some class’’ ...

The graph-colouring problem may be generalised by allowing arbitrary constraints to be speciied on the colour combinations permitted at each pair of adjacent nodes. A set of colourings which is the solution to some network of speciied constraints is said to be a representable set. This paper derives exact expressions for the number of representable sets when the corresponding graph is cycle-fre...

Series-parallel orders are deened as the least class of partial orders containing the one-element order and closed by ordinal sum and disjoint union. From this inductive deenition, it is almost immediate that any series-parallel order may be represented by an algebraic expression, which is unique up to the associativity of ordinal sum and to the associa-tivivity and commutativity of disjoint un...

*Correspondence: [email protected] 2School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, China Full list of author information is available at the end of the article Abstract Importance measure is an index for estimating the importance of an individual component or a group of components in a reliability system. So far, the importance measures for compon...

The concept of a defective circular coloring is introduced, and results shown for planar, series-parallel, and outerplanar graphs. Numerous problems are also stated.