In this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. We focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of Fomin and Reading, and colored quiver mutation.

The Sicilian Gambit: an opening move that loses the game? The Sicilian Gambit is the title of a review article on antiarrhythmic drug therapy published simultaneously in the European Heart Journal and Circulation in 1991 1 ' 1. The rather peculiar name is a reference to the Queen's Gambit (an opening move in chess) and the fact that the article, considered by the authors as an 'opening move' in...

A list of related materials, with annotations to guide further exploration of the article's ideas and applications 11 Further Reading A company's bid to rally an industry ecosystem around a new competitive view is an uncertain gambit. But the right strategic approaches and the availability of modern digital infrastructures improve the odds for success.

Fawcett et al. correctly identified a problem: despite repeated calls for a greater integration of psychological and biological approaches, most behavioral ecologists still study the evolution of behavioral strategies rather than the evolution of the learning mechanisms that produce or shape these strategies. The problem is not limited to foraging behavior. Nearly two decades ago, we demonstrat...

In Ziegler (2002), the second author presented a lower bound for the chromatic numbers of hypergraphs KG sS, “generalized r-uniform Kneser hypergraphs with intersection multiplicities s.” It generalized previous lower bounds by Kř́ıž (1992/2000) for the case s = (1, . . . , 1) without intersection multiplicities, and by Sarkaria (1990) for S = ([n] k ) . Here we discuss subtleties and difficulti...

The Grothendieck constant KG is the smallest constant such that for every d ∈ N and every matrix A = (aij),

Benjamin Kolbe studierte den Diplomstudiengang Informatik an der Fachhochschule Flensburg. Er bekam 2009 den Titel Diplom-Informatiker verliehen. Schon während des Studiums war er bei der Firma ITD Informationstechnologie GmbH & Co. KG als Werkvertragsnehmer tätig. Bei dieser Tätigkeit arbeitete er an verschiedenen Produkten im Bereich der Entwicklung von VoIP-Messsystemen. Außerdem war er für ...