We study two-player positional games where Maker and Breaker take turns to select a
previously unoccupied number in $\{1, 2,\ldots, n\} $. Maker wins if the numbers selected by …

For integers k, n with k, n⩾ 1, the n-color weak Schur number WS k (n) is defined as the least
integer N, such that for every n-coloring of the integer interval [1, N], there exists a …

Combinatorial Problems on the Integers: Colorings, Games, and Permutations A Dissertation
Presented to the Faculty of the Colleg Page 1 Combinatorial Problems on the Integers …

We study two-player positional games where Maker and Breaker take turns to select a
previously unoccupied number in {1, 2,..., n}. Maker wins if the numbers selected by Maker …

In this paper, we introduce a generalization of Schur numbers, analogous to the weakened
generalization of Ramsey numbers. Specifically, define WSk l (n) to be the least natural …

A hypothetical exclusion principle for quantum particles is introduced that generalizes the
exclusion and inclusion principles for fermions and bosons, respectively: the correlated …