Zobrazeno 1 - 10
of 96
pro vyhledávání: '"05D10, 05C55"'
Autor:
Ghosh, Arpita, Ghosh, Surojit
The set of sums of two squares plays an important role in the elementary number theory. Di Nasso investigated several infinite monochromatic patterns in integers considering operations induced from affine maps and asked whether one can find different
Externí odkaz:
http://arxiv.org/abs/2411.14066
A randomly perturbed graph $G^p = G_\alpha \cup G(n,p)$ is obtained by taking a deterministic $n$-vertex graph $G_\alpha = (V, E)$ with minimum degree $\delta(G)\geq \alpha n$ and adding the edges of the binomial random graph $G(n,p)$ defined on the
Externí odkaz:
http://arxiv.org/abs/2410.11003
Autor:
Dobák, Dániel, Mulrenin, Eion
The Erd\H{o}s-Rado canonization theorem generalizes Ramsey's theorem to edge-colorings with an unbounded number of colors, in the sense that for $n = ER(m)$ sufficiently large, any edge-coloring of $E(K_n) \to \mathbb{N}$ will yield some copy of $K_m
Externí odkaz:
http://arxiv.org/abs/2410.08982
In his study of graph codes, Alon introduced the concept of the odd-Ramsey number of a family of graphs $\mathcal{H}$ in $K_n$, defined as the minimum number of colours needed to colour the edges of $K_n$ so that every copy of a graph $H\in \mathcal{
Externí odkaz:
http://arxiv.org/abs/2410.05887
Autor:
Goswami, Sayan
In $1979$, using the theory of ultrafilters, N. Hindman proved that for every finite coloring of $\mathbb{N}$, there exists a color that contains both additive and multiplicative $IP$ sets. Later, in $1993$, V. Bergelson and N. Hindman found an eleme
Externí odkaz:
http://arxiv.org/abs/2407.05542
For graphs $F$ and $H$, let $f_{F,H}(n)$ be the minimum possible size of a maximum $F$-free induced subgraph in an $n$-vertex $H$-free graph. This notion generalizes the Ramsey function and the Erd\H{o}s--Rogers function. Establishing a container lem
Externí odkaz:
http://arxiv.org/abs/2406.13780
Autor:
Inamdar, Tanmay
We prove that for every colouring of pairs of reals with finitely-many colours, there is a set homeomorphic to the rationals which takes no more than two colours. This was conjectured by Galvin in 1970, and a colouring of Sierpi{\'n}ski from 1933 wit
Externí odkaz:
http://arxiv.org/abs/2405.18431
Autor:
Goswami, Sayan, Patra, Sourav Kanti
In this article, we prove twofold polynomial extension of Beigelb\"{o}ck's \cite{b} multidimensional Central Sets Theorem (which was a common extension of Furstenberg's Central Sets Theorem, and Milliken-Taylor theorem). We also find the complete ult
Externí odkaz:
http://arxiv.org/abs/2405.07296
In Euclidean Ramsey Theory usually we are looking for monochromatic configurations in the Euclidean space, whose points are colored with a fixed number of colors. In the canonical version, the number of colors is arbitrary, and we are looking for an
Externí odkaz:
http://arxiv.org/abs/2404.11454
Autor:
Goswami, Sayan
Recently M. Di Nasso and M. Ragosta proved an exponential version of Hindman's finite sum theorem: for every finite partition of $\mathbb{N}$, there exists a monochromatic Hindman tower of a single sequence. They used the stronger version of Furstenb
Externí odkaz:
http://arxiv.org/abs/2401.10550