Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
121 tokens/sec
GPT-4o
9 tokens/sec
Gemini 2.5 Pro Pro
47 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

New Bounds on Diffsequences (2110.10760v4)

Published 20 Oct 2021 in math.CO

Abstract: For a set of positive integers $D$, a $k$-term $D$-diffsequence is a sequence of positive integers $a_1<a_2<\cdots<a_k$ such that $a_i-a_{i-1}\in D$ for $i=2,3,\cdots,k$. For $k\in\mathbb{Z}+$ and $D\subset \mathbb{Z}+$, we define $\Delta(D,k)$, if it exists, to be the smallest integer $n$ such that every $2$-coloring of ${1,2,\cdots,n}$ contains a monochromatic $D$-diffsequence of length $k$. We improve the lower bound on $\Delta(D,k)$ where $D={2i\mid i\in\mathbb{Z}{\geq{0}}}$, proving a conjecture of Chokshi, Clifton, Landman, and Sawin. We also determine all sets of the form $D={d_1,d_2,\dots}$ with $d_i\mid d{i+1}$ for which $\Delta(D,k)$ exists.

Summary

We haven't generated a summary for this paper yet.