-adic analysis and Bell numbers of two variables. (Analyse -adique et nombres de Bell à deux variables.)
Partition statistics and -Bell numbers .
Partition-dependent stochastic measures and -deformed cumulants.
Partitions, rooks, and symmetric functions in noncommuting variables.
Pattern avoiding partitions and Motzkin left factors
Let L n, n ≥ 1, denote the sequence which counts the number of paths from the origin to the line x = n − 1 using (1, 1), (1, −1), and (1, 0) steps that never dip below the x-axis (called Motzkin left factors). The numbers L n count, among other things, certain restricted subsets of permutations and Catalan paths. In this paper, we provide new combinatorial interpretations for these numbers in terms of finite set partitions. In particular, we identify four classes of the partitions of size n, all...
Perfekte Dreieckzerlegungen.
Permutations which make transitive groups primitive
In this article we look into characterizing primitive groups in the following way. Given a primitive group we single out a subset of its generators such that these generators alone (the so-called primitive generators) imply the group is primitive. The remaining generators ensure transitivity or comply with specific features of the group. We show that, other than the symmetric and alternating groups, there are infinitely many primitive groups with one primitive generator each. These primitive groups...