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...
Records in set partitions.
Recurrence relations and two-dimensional set partitions.
Remarques sur la théorie des régions et des aspects
Restricted partitions and q-Pell numbers
In this paper, we provide new combinatorial interpretations for the Pell numbers p n in terms of finite set partitions. In particular, we identify six classes of partitions of size n, each avoiding a set of three classical patterns of length four, all of which have cardinality given by p n. By restricting the statistic recording the number of inversions to one of these classes, and taking it jointly with the statistic recording the number of blocks, we obtain a new polynomial generalization of p...
Rook theory, generalized Stirling numbers and -analogues.
Set partitions with successions and separations.
Sets, lists and noncrossing partitions.
Some combinatorics involving ξ-large sets
We prove a version of the Ramsey theorem for partitions of (increasing) n-tuples. We derive this result from a version of König's infinity lemma for ξ-large trees. Here ξ < ε₀ and the notion of largeness is in the sense of Hardy hierarchy.
Some summation formulae over the set of partitions.
Sur le problème des aspects
Symmetric partitions and pairings
The lattice of partitions and the sublattice of non-crossing partitions of a finite set are important objects in combinatorics. In this paper another sublattice of the partitions is investigated, which is formed by the symmetric partitions. The measure whose nth moment is given by the number of non-crossing symmetric partitions of n elements is determined explicitly to be the "symmetric" analogue of the free Poisson law.
Symmetric sum-free partitions and lower bounds for Schur numbers.
The asymptotic number of set partitions with unequal block sizes.
The complexity of retina operators.
The freeness of ideal subarrangements of Weyl arrangements
A Weyl arrangement is the arrangement defined by the root system of a finite Weyl group. When a set of positive roots is an ideal in the root poset, we call the corresponding arrangement an ideal subarrangement. Our main theorem asserts that any ideal subarrangement is a free arrangement and that its exponents are given by the dual partition of the height distribution, which was conjectured by Sommers–Tymoczko. In particular, when an ideal subarrangement is equal to the entireWeyl arrangement, our...
The number of certain -combinations of an -set.
The -Bell numbers.
The shape of a typical boxed plane partition.