Totally frustrated states in the chromatic theory of gain graphs

We generalize proper coloring of gain graphs to totally frustrated states, where each vertex takes a value in a set of `qualities' or `spins' that is permuted by the gain group. (An example is the Potts model.) The number of totally frustrated states satisfies the usual deletion-contraction law but is matroidal only for standard coloring, where the group action is trivial or nearly regular. One can generalize chromatic polynomials by constructing spin sets with repeated transitive components.Comment: 14 pages, 2 figure

On the Falk invariant of hyperplane arrangements attached to gain graphs

The fundamental group of the complement of a hyperplane arrangement in a complex vector space is an important topological invariant. The third rank of successive quotients in the lower central series of the fundamental group was called Falk invariant of the arrangement since Falk gave the first formula and asked to give a combinatorial interpretation. In this article, we give a combinatorial formula for the Falk invariant of hyperplane arrangements attached to certain gain graphs.Comment: To appear in the Australasian Journal of Combinatorics. arXiv admin note: text overlap with arXiv:1703.0940

RETHINKING ECONOMY-WIDE REBOUND MEASURES: AN UNBIASED PROPOSAL

In spite of having been first introduced in the last half of the ninetieth century, the debate about the possible rebound effects from energy efficiency improvements is still an open question in the economic literature. This paper contributes to the existing research on this issue proposing an unbiased measure for economy-wide rebound effects. The novelty of this economy-wide rebound measure stems from the fact that not only actual energy savings but also potential energy savings are quantified under general equilibrium conditions. Our findings indicate that the use of engineering savings instead of general equilibrium potential savings downward biases economy-wide rebound effects and upward-biases backfire effects. The discrepancies between the traditional indicator and our proposed measure are analysed in the context of the Spanish economy.

On the trade balance effects of free trade agreements between the EU-15 and the CEEC-4 countries

The expansion of regionalism has spawned an extensive theoretical literature analysing the effects of Free Trade Agreements (FTAs) on trade flows. In this paper we focus on FTAs (also called European agreements) between the European Union (EU-15) and the Central and Eastern European countries (CEEC-4, i.e. Bulgaria, Hungary, Poland and Romania) and model their effects on trade flows by treating the agreement variable as endogenous. Our theoretical framework is the gravity model, and the econometric method used to isolate and eliminate the potential endogeneity bias of the agreement variable is the fixed effect vector decomposition (FEVD) technique. Our estimation results indicate a positive and significant impact of FTAs on trade flows. However, exports and imports are affected differently, leading to some disparity in trade flow performance between countries. Therefore, there is an asymmetric impact on the trade balance, the agreement variable resulting in a trade balance deficit in the CEEC

Cycle and Circle Tests of Balance in Gain Graphs: Forbidden Minors and Their Groups

We examine two criteria for balance of a gain graph, one based on binary cycles and one on circles. The graphs for which each criterion is valid depend on the set of allowed gain groups. The binary cycle test is invalid, except for forests, if any possible gain group has an element of odd order. Assuming all groups are allowed, or all abelian groups, or merely the cyclic group of order 3, we characterize, both constructively and by forbidden minors, the graphs for which the circle test is valid. It turns out that these three classes of groups have the same set of forbidden minors. The exact reason for the importance of the ternary cyclic group is not clear.Comment: 19 pages, 3 figures. Format: Latex2e. Changes: minor. To appear in Journal of Graph Theor