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We prove that the monoid of generic extensions of finite-dimensional nilpotent k[T]-modules is isomorphic to the monoid of partitions (with addition of partitions). This gives us a simple method for computing generic extensions, by addition of partitions. Moreover we give a combinatorial algorithm that calculates the constant terms of classical Hall polynomials.

Geometry of links.

Jablan, Slavik V. (1999)

Novi Sad Journal of Mathematics

Good lower and upper bounds on binomial coefficients.

Stănică, Pantelimon (2001)

JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]

Graph compositions. I: Basic enumeration.

Knopfmacher, A., Mays, M.E. (2001)

Integers

Graph weights arising from Mayer's theory of cluster integrals.

Labelle, Gilbert, Leroux, Pierre, Ducharme, Martin G. (2005)

Séminaire Lotharingien de Combinatoire [electronic only]

Graphical condensation, overlapping Pfaffians and superpositions of matchings.

Fulmek, Markus (2010)

The Electronic Journal of Combinatorics [electronic only]

Graphical major indices. II.

Foata, Dominique, Krattenthaler, Christian (1995)

Séminaire Lotharingien de Combinatoire [electronic only]

Graphs $S (n, k)$ and a variant of the Tower of Hanoi problem

Sandi Klavžar, Uroš Milutinović (1997)

Czechoslovak Mathematical Journal

For any $n \geq 1$ and any $k \geq 1$ , a graph $S (n, k)$ is introduced. Vertices of $S (n, k)$ are $n$ -tuples over ${1, 2, ..., k}$ and two $n$ -tuples are adjacent if they are in a certain relation. These graphs are graphs of a particular variant of the Tower of Hanoi problem. Namely, the graphs $S (n, 3)$ are isomorphic to the graphs of the Tower of Hanoi problem. It is proved that there are at most two shortest paths between any two vertices of $S (n, k)$ . Together with a formula for the distance, this result is used to compute the distance between two vertices in...

Gray codes for $A$ -free strings.

Squire, Matthew B. (1996)

The Electronic Journal of Combinatorics [electronic only]

Gray codes in graphs

Martin Knor (1994)

Mathematica Slovaca

Green's Relations in Finnite Function Semigroups

JOHN BAILLIEUL (1971)

Aequationes mathematicae

Grid classes and the Fibonacci dichotomy for restricted permutations.

Huczynska, Sophie, Vatter, Vincent (2006)

The Electronic Journal of Combinatorics [electronic only]

Gromov hyperbolic cubic graphs

Domingo Pestana, José Rodríguez, José Sigarreta, María Villeta (2012)

Open Mathematics

If X is a geodesic metric space and x 1; x 2; x 3 ∈ X, a geodesic triangle T = {x 1; x 2; x 3} is the union of the three geodesics [x 1 x 2], [x 2 x 3] and [x 3 x 1] in X. The space X is δ-hyperbolic (in the Gromov sense) if any side of T is contained in a δ-neighborhood of the union of the two other sides, for every geodesic triangle T in X. We denote by δ(X) the sharp hyperbolicity constant of X, i.e., δ(X) = inf {δ ≥ 0: X is δ-hyperbolic}. We obtain information about the hyperbolicity constant...

Gromov hyperbolicity of planar graphs

Alicia Cantón, Ana Granados, Domingo Pestana, José Rodríguez (2013)

Open Mathematics

We prove that under appropriate assumptions adding or removing an infinite amount of edges to a given planar graph preserves its non-hyperbolicity, a result which is shown to be false in general. In particular, we make a conjecture that every tessellation graph of ℝ2 with convex tiles is non-hyperbolic; it is shown that in order to prove this conjecture it suffices to consider tessellation graphs of ℝ2 such that every tile is a triangle and a partial answer to this question is given. A weaker version...

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