We describe some combinatorial problems in finite projective planes and indicate how Rédei’s theory of lacunary polynomials can be applied to them. 2000 Mathematics Subject Classification: 05.

In this paper, we study the Lehmer’s type congruences for lacunary harmonic sums.

<p style='text-indent:20px;'>A set <inline-formula><tex-math id="M1">\begin{document}$ E \subset \mathbb{N} $\end{document}</tex-math></inline-formula> is an interpolation for nilsequences if every bounded function on id="M2">\begin{document}$ can be extended to a nilsequence id="M3">\begin{document}$ $\end{document}</tex-math></inline-formula>. F...

in this paper, under the condition that $k$ is concave, we characterize lacunary series in $q_{k}$ spaces. we improve a result due to h. wulan and k. zhu.

Lacunary polyoxometalates (POMs) are negatively charged metal–oxo clusters, formally obtained from plenary topologies via fragment removal. Owing to the removal, lacunary POMs archetypes rich in nucleophilic terminal oxo ligands, making them suitable for post-synthetic coordination with various heterometals. Trilacunary heteropolytungstates (hetero-POTs) based on bowl-shaped {W9O30} framework i...

Let {theta(j)} be a lacunary sequence going to zero. Let [Formula: see text]. Define [Formula: see text]. We prove [Formula: see text].