This is an announcement for the paper "Minimal sequences and the Kadison-Singer problem" by W. Lawton. Abstract: The Kadison-Singer problem asks: does every pure state on the C$^*$-algebra $\ell^{\infty}(Z)$ admit a unique extension to the C$^*$-algebra $\cB(\ell^2(Z))$? A yes answer is equivalent to several open conjectures including Feichtinger's: every bounded frame is a finite union of Riesz sequences. We prove that for measurable $S \subset \TT,$ $\{ \chi_{_S} \, e^{2\pi i k t} \}_{_{k\in \ZZ}}$ is a finite union of Riesz sequences in $L^2(\TT)$ if and only if there exists a nonempty $\Lambda \subset \ZZ$ such that $\chi_{_\Lambda}$ is a minimal sequence and $\{ \chi_{_S} \, e^{2\pi i k t} \}_{_{k \in \Lambda}}$ is a Riesz sequence. We also suggest some directions for future research. Archive classification: math.FA math.DS Mathematics Subject Classification: 37B10, 42A55, 46L05 Remarks: 10 pages, Theorem 1.1 was announced during conferences in St. The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/0911.5559 or http://arXiv.org/abs/0911.5559 or by email in unzipped form by transmitting an empty message with subject line uget 0911.5559 or in gzipped form by using subject line get 0911.5559 to: math@arXiv.org.