Related papers: A note on the induced Ramsey theorem for spaces

The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.

Segre's theorem on ovals in projective spaces is an ingenious result from the mid-twentieth century which requires surprisingly little background to prove. This note, suitable for undergraduates with experience of linear and abstract…

We construct a Ramsey class whose objects are Steiner systems. In contrast to the situation with general $r$-uniform hypergraphs, it turns out that simply putting linear orders on their sets of vertices is not enough for this purpose: one…

We translate the main theorem in Tom McKay's paper "On plethysm conjectures of Stanley and Foulkes" (J. Alg. 319, 2008, pp. 2050-2071) to the language of weight spaces and projections onto invariant spaces of tensors, which makes its proof…

Represented spaces form the general setting for the study of computability derived from Turing machines. As such, they are the basic entities for endeavors such as computable analysis or computable measure theory. The theory of represented…

For a partially ordered set $(A, \le)$, let $G_A$ be the simple, undirected graph with vertex set $A$ such that two vertices $a \neq b\in A$ are adjacent if either $a \le b$ or $b \le a$. We call $G_A$ the \emph{partial order graph} or…

The note clarifies a gap in the proof of the minimum distance for Projective Reed-Muller Codes. The gap was identified by S.Ghorpade and R.Ludhani in a recent article. Here the original thoughts are explained and the gap closed.

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

The main aim of this note is to derive necessary and sufficient conditions for the convergence of Fej\'er means in terms of the modulus of continuity of the Hardy spaces $H_{p},$ $\left(0<p\leq 1\right)$.

In literature, the central limit theorems for the product of sums of various random variables have studied. The purpose of this note is to show that this kind of results are corollary of the invariance principle.

A new linear mapping of the linear vector space (LVS) of the octonions is suggested as an approach to the co-ordinatization of space-time. This approach resolves some perplexing issues concerning the validity of certain pre-metric notions…

We develop the theory of Fra\"iss\'e limits for classes of finite-dimensional multi-seminormed spaces, which are defined to be vector spaces equipped with a finite sequence of seminorms. We define a notion of a Fra\"iss\'e Fr\'echet space…

In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.

We introduce the ramified partition algebra, which is a physically motivated and natural generalization of the partition algebra. We investigate its representation theory and demonstrate quasi--heredity under certain conditions. Under these…

A proof of Sharkovsky's Theorem is given. It is shown how this proof naturally generalizes to looking at maps on graphs and to Sharkovsky-type theorems for these maps. The paper is written at an elementary level and is meant as an…

This the first of a set of three papers about the Compression Theorem: if M^m is embedded in Q^q X R with a normal vector field and if q-m > 0, then the given vector field can be straightened (ie, made parallel to the given R direction) by…

We prove the Ramsey property for classes of ordered structures with closures and given local properties. This generalises earlier results: the Ne\v{s}et\v{r}il-R\"odl Theorem, the Ramsey property of partial orders and metric spaces as well…

We propose a slight correction and a slight improvement on the main result contained in "A lecture on Classical KAM Theorem" by J. P{\"o}schel.

We prove a new characterization of the Ramsey property of categories in terms of a generalized form of K\H{o}nig's tree lemma. Afterwards, we discuss its applications to structural Ramsey theory. In particular, we provide a new proof of the…

In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…