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.
Topological multidimensional van der Waerden theorem
Two analogues of a classical sequence.
Two statistics linking Dyck paths and non-crossing partitions.