 
Summary: ISRAEL JOURNAL OF MATHEMATICS 167 (2008), 177191
DOI: 10.1007/s1185600810466
SHELLABILITY AND HIGHER
COHENMACAULAY CONNECTIVITY OF
GENERALIZED CLUSTER COMPLEXES
BY
Christos A. Athanasiadis
Department of Mathematics (Division of AlgebraGeometry), University of Athens
Panepistimioupolis, 15784 Athens, Greece
email: caath@math.uoa.gr
AND
Eleni Tzanaki
Department of Mathematics, University of Crete
71409 Heraklion, Crete, Greece
email: etzanaki@math.uoc.gr
ABSTRACT
Let be a finite root system of rank n and let m be a nonnegative integer.
The generalized cluster complex m() was introduced by S. Fomin and
N. Reading. It was conjectured by these authors that m() is shellable
and by V. Reiner that it is (m + 1)CohenMacaulay, in the sense of Ba
