On the uniform generation of modular diagrams.
On the volume of a certain polytope.
On the volume of the polytope of doubly stochastic matrices.
On two combinatorial identities
On two supercongruences involving Almkvist-Zudilin sequences
We prove two supercongruences involving Almkvist-Zudilin sequences, which were originally conjectured by Z.-H. Sun (2020).
On unimodality problems in Pascal's triangle.
On useful schema in survival analysis after heart attack
Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers
On weak convergence of sequences of measures
On Zeilberger's constant term for Andrew's TSSCPP theorem.
One-dimensional game of life and its growth functions.
One-pile misère Nim for three or more players.
On-line Ramsey theory.
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.