Generating functions for the digital sum and other digit counting sequences.
Generating functions for the number of permutations with limited displacement.
Generating functions for Wilf equivalence under generalized factor order.
Generating functions related to partition formulæ for Fibonacci numbers.
Generating functions via Hankel and Stieltjes matrices.
Generating random elements of finite distributive lattices.
Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials
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.
Good lower and upper bounds on binomial coefficients.
Graph compositions. I: Basic enumeration.
Graph weights arising from Mayer's theory of cluster integrals.
Graphical condensation, overlapping Pfaffians and superpositions of matchings.
Graphical major indices. II.
Graphs and a variant of the Tower of Hanoi problem
For any and any , a graph is introduced. Vertices of are -tuples over and two -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 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 . Together with a formula for the distance, this result is used to compute the distance between two vertices in...
Gray codes for -free strings.
Gray codes in graphs
Green's Relations in Finnite Function Semigroups
Grid classes and the Fibonacci dichotomy for restricted permutations.
Gromov hyperbolic cubic graphs
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
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...