Related papers: On the Erdos-Fuchs theorem
We provide new sufficient conditions under which Ryser's conjecture holds.
We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.
In this article, we go on to discuss about a series of infinite dimensional extension of the theorems in [3], [5], [6]. We also prove a similar Geraghty type constructions for Fisher ([5]) in infinite dimension, using similar techniques as…
We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.
We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.
We survey the classical results of the Dirichlet Approximation Theorem.
We give a new proof of Lucas' Theorem in elementary number theory.
We establish a variety of extensions to the Erdos-Rado Theorem, particularly involving ordinal numbers, and always involving ordinary partition relations. Most of the results can be regarded as consequences of the Ramification Principle,…
We extend the famous Erd\H{o}s-Szekeres theorem to $k$-flats in ${\mathbb{R}^d}$
We prove Union-Closed sets conjecture.
In this note a far extension of the Banach fixed point theorem is proved.
We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.
Our main theorem is an extension of the well-known Mizoguchi-Takahaashi's fixed point theorem [N. Mizogochi and W. Takahashi, Fixed point theorems for multi-valued mappings on complete metric space, {\it J. Math. Anal. Appl.} 141 (1989)…
In this paper, we give a refinement of a theorem by Franks, which answers two questions raised by Kang.
We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.
Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
We generalize Rado's extension theorem to complex spaces.
This is a short historical note concerning the evolution of Wetzel's problem and Erdos' solution.
We prove an extension of the Thue-Vinogradov Lemma and show some applications. This paper is another example for the application of the polynomial method.