This is an announcement for the paper "Block combinatorics" by V. Farmaki and S. Negrepontis. Abstract: In this paper we extend the block combinatorics partition theorems of Hindman and Milliken in the setting of the recursive system of the block Schreier families (B^xi) consisting of families defined for every countable ordinal xi. Results contain (a) a block partition Ramsey theorem for every countable ordinal xi (Hindman's theorem corresponding to xi=1, and Milliken's theorem to xi a finite ordinal), (b) a countable ordinal form of the block Nash-Williams partition theorem, and (c) a countable ordinal block partition theorem for sets closed in the infinite block analogue of Ellentuck's topology. Archive classification: Combinatorics; Functional Analysis Mathematics Subject Classification: 05D10; 46B20 Remarks: 26 pages, AMS-LaTeX The source file(s), fn04.tex: 83752 bytes, is(are) stored in gzipped form as 0406188.gz with size 20kb. The corresponding postcript file has gzipped size 98kb. Submitted from: combs@mail.ma.utexas.edu The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/math.CO/0406188 or http://arXiv.org/abs/math.CO/0406188 or by email in unzipped form by transmitting an empty message with subject line uget 0406188 or in gzipped form by using subject line get 0406188 to: math@arXiv.org.