This is an announcement for the paper "Rearrangements with supporting trees, isomorphisms and combinatorics of coloured dyadic intervals" by Anna Kamont and Paul F. X. Mueller. Abstract: We determine a class of rearrangements that admit a supporting tree. This condition implies that the associated rearrangement operator has a bounded vector valued extension. We show that there exists a large subspace of $L^p$ on which a bounded rearrangement operator acts as an isomorphism. The combinatorial issues of these problems give rise to a two-person game, to be played with colored dyadic intervals. We determine winning strategies for each of the players. Archive classification: math.FA Mathematics Subject Classification: 46B25; 46E40; 91A05 The source file(s), buch.def: 1005 bytes isoplussept091.bbl: 5771 bytes isoplussept091.tex: 98057 bytes math111.def: 7238 bytes, is(are) stored in gzipped form as 0909.4926.tar.gz with size 32kb. The corresponding postcript file has gzipped size 170kb. Submitted from: pfxm@bayou.uni-linz.ac.at The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0909.4926 or http://arXiv.org/abs/0909.4926 or by email in unzipped form by transmitting an empty message with subject line uget 0909.4926 or in gzipped form by using subject line get 0909.4926 to: math@arXiv.org.