10 citations · 13 across the 7 of their papers we have counts for
15 papers
Saturated chains in composition posets
Jan Snellman
We study three different poset structures on the set of all compositions. In the first case, the covering relation consists of inserting a part of size one to the left or to the ri…
Standard paths in another composition poset
Jan Snellman
Bergeron, Bousquet-Melou and Dulucq enumerated paths in the Hasse diagram of the following poset: the underlying set is that of all compositions, and a composition μcovers another…
Enumeration of concave integer partitions
Jan Snellman, Michael Paulsen
An integer partition λof n corresponds, via its Ferrers diagram, to an artinian monomial ideal I of colength n in the polynomial ring on two variables. If the partition λcorrespond…
Simplicial complexes associated to certain subsets of natural numbers and its applications to multiplicative functions
Jan Snellman
We call a set of positive integers closed under taking unitary divisors a unitary ideal. It can be regarded as a simplicial complex. Moreover, a multiplicative arithmetical functio…
The maximal spectral radius of a digraph with (m+1)^2 - s edges
Jan Snellman
It is known that the spectral radius of a digraph with k edges is \le \sqrt{k}, and that this inequality is strict except when k is a perfect square. For k=m^2 + \ell, \ell fixed,…
The ring of arithmetical functions with unitary convolution: the [n]-truncation
Jan Snellman
We study a certain truncation of the ring of arithmetical functions with unitary convolution, consisting of functions vanishing on arguments >n. The truncations are artinian monomi…