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- Jan Snellman
- Electr. J. Comb.
- 2004

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)

- Jan Snellman
- J. Symb. Comput.
- 1998

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)

- Jan Snellman
- 1997

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)

- Jan Snellman
- 1999

- JAN SNELLMAN
- 2001

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)

- JAN SNELLMAN
- 1998

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)

- Jan Snellman
- 1997

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)

- Jan Snellman
- 2003

It is known that the spectral radius of a digraph with k edges is ≤ √ k, and that this inequality is strict except when k is a perfect square. For k = m + l, l fixed, m large, Friedland showed that the optimal digraph is obtained from the complete digraph onm vertices by adding one extra vertex, and a corresponding loop, and then connecting it to the first… (More)

- JAN SNELLMAN
- 2002

We study a certain truncationA[n] of the ring of arithmetical functions with unitary convolution, consisting of functions vanishing on arguments > n. The truncations A[n] are artinian monomial quotients of a polynomial ring in finitely many indeterminates, and are isomorphic to the “artinified” Stanley-Reisner ring C[∆([n])] of a simplicial complex ∆([n]).