Jan Snellman

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Bergeron, Bousquet-Mélou and Dulucq [1] enumerated paths in the Hasse diagram of the following poset: the underlying set is that of all compositions, and a composition μ covers another composition λ if μ can be obtained from λ by adding 1 to one of the parts of λ, or by inserting a part of size 1 into λ. We employ the methods they developed in order to(More)
If K is a field, let the ring R′ consist of finite sums of homogeneous elements in R = K[[x1, x2, x3, . . .]]. Then, R′ contains M, the free semi-group on the countable set of variables {x1, x2, x3, . . .}. In this paper, we generalize the notion of admissible order from finitely generated sub-monoids of M to M itself; assume that > is such an admissible(More)
Denote by R the power series ring in countably many variables over a eld K; then R 0 is the smallest sub-algebra of R that contains all homogeneous elements. It is a fact that a homogeneous, nitely generated ideal J in R 0 have an initial ideal gr(J), with respect to an arbitrary admissible order, that is locally nitely generated in the sense that dimK(More)
We study a poset N on the free monoid X∗ on a countable alphabet X. This poset is determined by the fact that its total extensions are precisely the standard term orders on X ∗. We also investigate the poset classifying degree-compatible standard term orders, and the poset classifying sorted term orders. For the latter poset, we give a Galois coconnection(More)
We study two partial orders on [x1, . . . , xn], the free abelian monoid on {x1, . . . , xn}. These partial orders, which we call the “strongly stable” and the “stable” partial order, are defined by the property that their filters are precisely the strongly stable and the stable monoid ideals. These ideals arise in the study of generic initial ideals.
An integer partition λ ` n corresponds, via its Ferrers diagram, to an artinian monomial ideal I ⊂ C[x, y] with dimC C[x, y]/I = n. If λ corresponds to an integrally closed ideal we call it concave . We study generating functions for the number of concave partitions, unrestricted or with at most r parts. 1. concave partitions By an integer partition λ =(More)
If K is a eld, let the ring R 0 consist of nite sums of homogeneous elements in R = Kx 1 ; x 2 ; x 3 ; : : : ]]. Then, R 0 contains M, the free semi-group on the countable set of variables fx 1 ; x 2 ; x 3 ; : : :g. In this paper, we generalize the notion of admissible order from nitely generated sub-monoids of M to M itself; assume that > is such an(More)