10 citations · 13 across the 7 of their papers we have counts for
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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,…
A poset classifying non-commutative term orders
Jan Snellman
We study a certain poset on the free monoid on a countable alphabet. This poset is determined by the fact that its total extensions are precisely the standard term orders. We also…