{sl Let $[n]={1,dots, n}$ be colored in $k$ colors. A rainbow AP$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. Conlon, Jungi'{c} and Radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow AP(4) free, when $n$ is even. Based on their construction, we show that such a coloring of $[4n]$...

{sl let $[n]={1,dots, n}$ be colored in $k$ colors. a rainbow ap$(k)$ in $[n]$ is a $k$ term arithmetic progression whose elements have different colors. conlon, jungi'{c} and radoiv{c}i'{c} cite{conlon} prove that there exists an equinumerous 4-coloring of $[4n]$ which is rainbow ap(4) free, when $n$ is even. based on their construction, we show that such a coloring of ...

Sinead N. Duggan BSc., Research Dietitian Kevin C. Conlon MD, Chair of Surgery Centre for Pancreatico-Biliary Diseases, Tallaght Hospital & Trinity College, Dublin, Ireland Chronic pancreatitis is a progressive inflammatory disease that results in the irreversible deterioration of exocrine and endocrine function. Although research is limited, patients with chronic pancreatitis are deemed at hig...

Two years ago, Conlon and Gowers, and Schacht proved general theorems that allow one to transfer a large class of extremal combinatorial results from the deterministic to the probabilistic setting. Even though the two papers solve the same set of long-standing open problems in probabilistic combinatorics, the methods used in them vary significantly and therefore yield results that are not compa...

A recent breakthrough of Conlon and Ferber yielded an exponential improvement on the lower bounds for multicolor diagonal Ramsey numbers. In this note, we modify their construction obtain improved more than three colors.

This paper presents the author’s heretofore unpublished example of nonisomorphic transitive permutation representations with isomorphic integral permutation modules. Some positive results are also given. This paper is dedicated to the menory of Hans Zassenhaus. Let G be a finite group acting on finite sets R,R’. Recall that R z R’ as G-sets if and only if there is a 1-l correspondence between 0...