Multinomial identities arising from the free probability theory

We prove a family of new identities fulfilled by multinomial coefficients, which were conjectured by Dykema and Haagerup. Our method bases on a study of the, so-called, triangular operator T by the means of the free probability theory.Comment: 20 pages; figures in PSTrick

Riots, coups and civil war : revisiting the greed and grievance debate

The most influential recent work on the determinants of civil wars found the factors associated with the grievance motivation to be largely irrelevant. Our paper subjects the results of this empirical work to further scrutiny by embedding the study of civil war in a more general analysis of varieties of violent contestation of political power within the borders of the state. Such an approach, we argue, will have important implications for how we think theoretically about the occurrence of domestic war as well as how we specify our empirical tests. In the empirical model, the manifestation of domestic conflict range from low intensity violence and coups to civil war. Our multinomial specification of domestic conflict supports the hypothesis that diversity accentuates distributional conflict and thus increases the risk of civil war. We also find that democracies may be more efficient than autocracies in reducing the risk of civil war.Post Conflict Reconstruction,Population Policies,Social Conflict and Violence,Peace&Peacekeeping,Hazard Risk Management

Sequences with long range exclusions

Given an alphabet $S$, we consider the size of the subsets of the full sequence space $S^{\rm {\bf Z}}$ determined by the additional restriction that $x_i\not=x_{i+f(n)},\ i\in {\rm {\bf Z}},\ n\in {\rm {\bf N}}.$ Here $f$ is a positive, strictly increasing function. We review an other, graph theoretic, formulation and then the known results covering various combinations of $f$ and the alphabet size. In the second part of the paper we turn to the fine structure of the allowed sequences in the particular case where $f$ is a suitable polynomial. The generation of sequences leads naturally to consider the problem of their maximal length, which turns out highly random asymptotically in the alphabet size.Comment: 18 pages, 3 figures. Replaces earlier version, submission 1204.3439, major updat

The Microstates Free Entropy Dimension of any DT--operator is 2

Suppose that \mu is an arbitrary Borel measure on the complex plane with compact support and take c > 0. If Z is a DT(\mu,c)-operator as defined by Dykema and Haagerup, then the microstates free entropy dimension of Z is 2Comment: 11 page