%0 Journal Article %T AN INTRODUCTION TO HIGHER CLUSTER CATEGORIES %J Bulletin of the Iranian Mathematical Society %I Iranian Mathematical Society (IMS) %Z 1017-060X %A BUAN, A. %D 2011 %\ 07/15/2011 %V 37 %N No. 2 %P 137-157 %! AN INTRODUCTION TO HIGHER CLUSTER CATEGORIES %K Cluster categories %K tilting %K triangulated categories %R %X 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. %U http://bims.iranjournals.ir/article_329_995a3b87119ae4d18ab2fb1a2224a40c.pdf