Operads and algebraic combinatorics of trees.
Operatorenkalkül über freien Monoiden I: Strukturen.
Operatorenkalkül über freien Monoiden II: Binominalsysteme.
Operatorenkalkül über freien Monoiden III: Lagrangeinversion und Sheffersysteme.
Operatormethoden für q-Identitäten.
Operatormethoden für q-Identitäten II: q-Laguerre Polynome.
Optimal bounds for the colored Tverberg problem
We prove a “Tverberg type” multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of Bárány et al. (1980), by adding color constraints. It also provides an improved bound for the (topological) colored Tverberg problem of Bárány & Larman (1992) that is tight in the prime case and asymptotically optimal in the general case. The proof is based on relative equivariant obstruction theory.
Optimal matrices of partitions and an application to Souslin trees
The basic result of this note is a statement about the existence of families of partitions of the set of natural numbers with some useful properties, the n-optimal matrices of partitions. We use this to improve a decomposition result for strongly homogeneous Souslin trees. The latter is in turn applied to separate strong notions of rigidity of Souslin trees, thereby answering a considerable portion of a question of Fuchs and Hamkins.
Optimal Penney Ante strategy via correlation polynomial identities.
Orders with ten elements are circle order.
Orthogonal partitions
Orthogonal partitions and covering of graphs
Osculating paths and oscillating tableaux.