complexity – nullteilerfrei

Binary Determinantal Complexity

rattle code, mathematics 2014-11-11

My good friend and colleague Christian Ikenmeyer and I wrote this cute preprint about polynomials and how they can be written as the determinant of a matrix with entries equal to zero, one and indeterminantes. Go ahead and read it if you know even just a little math, it's quite straightforward. The algorithm described in section 3 has been implemented and you can download the code from my website at the TU Berlin. Compilation instructions are in ptest.c, but you will need to get nauty to perform the entire computerized proof.

Scott McKenzie all the way

rattle mathematics, remark 2014-08-31

Even though this does not really constitute a post with substantial content, this is a blog after all, so I thought I'd let the 8 people who read it know that for the next six weeks, I will be attending a special semester on Algorithms and Complexity in Algebraic Geometry at the Simons Institute for the Theory of Computing in Berkeley. So. If you happen to be in the bay area, give me a shout.

Das Master Theorem

rattle mathematics 2014-05-06

Ich habe letzte Woche versucht, für einige Studenten das Master Theorem zu beweisen. Das ist geringfügig daneben gegangen, deswegen habe ich eine korrigierte Version des Beweises erstellt. Ich frage mich nun aber schon, wie allgemein man das eigentlich machen sollte. Grundsätzlich könnte man sich für eine Laufzeitfunktion $T:\mathbb N\to\mathbb N$ ja Rekurrenzgleichungen der Form $T = \alpha \circ T \circ \beta$ ansehen, wobei in meinem Fall $\beta(n)=n/b$ und $\alpha(n)=a\cdot n + f(n)$ ist. Ich habe leider keine Zeit, mir dazu mehr Gedanken zu machen.