Counting perfect matchings in polyominoes with an application to the dimer problem
Some postage stamp 2-bases.
The Blasius function in the complex plane.
Indecomposable tilings of the integers with exponentially long periods.
Multiple tilings of with long periods, and tiles with many-generated level semigroups.
On sot hat represents and and not .
On so that .
A non graph theory approach to Ulam's conjecture
Two Selection Theorems
Metrics for multivariate stable distributions
Metrics are proposed for the distance between two multivariate stable distributions. The first set of metrics are defined in terms of the closeness of the parameter functions of one dimensional projections of the laws. Convergence in these metrics is equivalent to convergence in distribution and an explicit bound on the uniform closeness of two stable densities is given. Another metric based on the Prokhorov metric between the spectral measures is related to the first metric. Consequences for approximation,...
Some extremal postage stamp bases.
Differentiable semigroups are Lie groups.
Descriptive Set Theory and Infinitary Languages
Periodic maps on Poincaré duality spaces.
PROBLEMS
On fundamental solutions of binary quadratic form equations
We show that, with suitable modification, the upper bound estimates of Stolt for the fundamental integer solutions of the Diophantine equation Au²+Buv+Cv²=N, where A>0, N≠0 and B²-4AC is positive and nonsquare, in fact characterize the fundamental solutions. As a corollary, we get a corresponding result for the equation u²-dv²=N, where d is positive and nonsquare, in which case the upper bound estimates were obtained by Nagell and Chebyshev.
On combinatorial isotopy
A slow-growing sequence defined by an unusual recurrence.
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