On Stanley-Wilf limit of the pattern 1324

Date: May 2021

Abstract: We use the Mansour-Vainshtein theory of kernel shapes to decompose the set of 1324-avoiding permutations of length n into small pieces that are governed by some kernel shape λ. This allows us to write down a systematic procedure for finding a lower bound for approximating the Stanley-Wilf limit of the pattern 1324. We use an implementation of this method in the OpenCL framework to compute such a bound explicitly.

On the secondary Steenrod algebra

Date: Nov 2010

Abstract: We introduce a new model for the secondary Steenrod algebra at the prime 2 which is both smaller and more accessible than the original construction of H.-J. Baues. We also explain how BP can be used to define a variant of the secondary Steenrod algebra at odd primes.

(Published in Volume 18 of the New York Journal of Mathematics.)

Ein neuer Algorithmus zur Untersuchung der Kohomologie der Steenrod-Algebra

Appeared: Logos Verlag Berlin 2002, ISBN 3-89722-881-5
Date: Feb 2002

Abstract: My PhD thesis. It develops an improved method for the computation of the minimal resolution of the Steenrod algebra. The algorithm is based on some well-known vanishing theorems for the cohomology of its sub Hopf algebras.

On the structure of P(n)*P(n) for p=2

Appeared: Trans. Amer. Math. Soc. 354
File(s): pnpnalg.dvi
Date: undated

Abstract: We show how the non-commutativity of P(n) for p=2 leads to complications in the algebra of cooperations P(n)*P(n).

Eine nichtgeometrische Konstruktion der Spektren P(n) und Multiplikative Automorphismen von K(n)

Appeared: Johann Wolfgang Goethe Universität Frankfurt, 1995
File(s): diplom.dvi
Date: Oct 1995

Abstract:My diploma thesis.