Published in Periodica Mathematica Hungarica
I give fully detailed proofs of two important theorems—the exact solution of the weak clique game and the compactness theorem—in the theory of positional games. Both results were published several years ago, including an outline of the proofs that explained the basic idea, but left some technical details to the reader. Unfortunately, in both cases ...
Published in Periodica Mathematica Hungarica
We study Hermite interpolation problems on the exponential curve y=ex\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$y=e^x$$\end{document} in R2\documentclass[12pt]{min...
Published in Periodica Mathematica Hungarica
Let G be a finite group and G′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$G'$$\end{document} its commutator subgroup. By a sequence over G, we mean a finite unorder...
Published in Periodica Mathematica Hungarica
For an irrational α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document}, we investigate the sums ∑i=1n{iα}-12\documentclass[12pt]{minimal} \usepackag...
Published in Periodica Mathematica Hungarica
A sum-and-distance system is a collection of finite sets of integers such that the sums and differences formed by taking one element from each set generate a prescribed arithmetic progression. Such systems, with two component sets, arise naturally in the study of matrices with symmetry properties and consecutive integer entries. Sum systems are an ...
Published in Periodica Mathematica Hungarica
We interpret the Combinatorial Nullstellensatz of Noga Alon as a multidimensional residue formula, describe some consequences of this interpretation and related open problems.
Published in Periodica Mathematica Hungarica
We discuss the generalized Kurepa hypothesis KHλ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{\mathrm{KH}}}_{\lambda }$$\end{document} at singular cardinals λ\docum...
Published in Periodica Mathematica Hungarica
Let S be the set of subsequences (xnk)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(x_{n_k})$$\end{document} of a given real sequence (xn)\documentclass[12pt]{minima...
Published in Periodica Mathematica Hungarica
Two new asymmetric generalizations of the Filbert and Lilbert matrices constructed by the products of two Fibonacci and Lucas numbers are considered, with additional parameter settings. Explicit formulæ are derived for their LU-decompositions and inverses.
Published in Periodica Mathematica Hungarica
The arithmetic Kakeya conjecture, formulated by Katz and Tao (Math Res Lett 6(5–6):625–630, 1999), is a statement about addition of finite sets. It is known to imply a form of the Kakeya conjecture, namely that the upper Minkowski dimension of a Besicovitch set in Rn\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage...
