C. Gaiser

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6 papers · 1 filter

math.CO2026

Restricted generalized Schur numbers

Collier Gaiser

For $k \geq 2$ , let $S_{r} (k; ℓ)$ be the smallest $n$ , if exists, such that every $r$ -coloring of ${1, 2, \dots, n}$ has a monochromatic solution $S$ to the equation \[ x_1…

math.CO2026

Pattern avoidance in permutations and their rotations

Ãmer EÄecioÄlu, Collier Gaiser, Mei Yin

A rotation of a permutation is a new permutation obtained by moving the first several terms of the permutation to the end of the permutation. A circular permutation is the set of a…

math.CO2026

A sharp lower bound for some reciprocal Rado numbers

Collier Gaiser, Mojtaba Ramezanpour

Let $f_{r} (k)$ be the smallest $n$ such that every $r$ -coloring of ${1, 2, \dots, n}$ has a monochromatic solution to the equation \[\frac{1}{x_1}+\frac{1}{x_2}+\cdots+\frac{1}{x_k}=…

math.CO2026

Subsequence sums in permutations

Collier Gaiser, Paul Horn

A sequence of positive integers $(a_{1}, a_{2}, \dots, a_{k})$ is called $ℓ$ -additive if $a_{1} + a_{2} + \dots + a_{k} = ℓ a_{1}$ or $ℓ a_{k}$ . In this paper, we prove that for all $k \geq 3$ , if $…

math.CO2026

Enumerating pattern-avoiding permutations by leading terms

Ãmer EÄecioÄlu, Collier Gaiser, Mei Yin

The number of 123-avoiding permutation on ${1, 2, \dots, n}$ with a fixed leading terms is counted by the ballot numbers. The same holds for $132$ -avoiding permutations. These resu…

math.CO2024

On Rado numbers for equations with unit fractions

Collier Gaiser

Let $f_{r} (k)$ be the smallest positive integer $n$ such that every $r$ -coloring of ${1, 2, ..., n}$ has a monochromatic solution to the nonlinear equation \[1/x_1+\cdots+1/x_k=1/y,\]…