相关论文: Adjacent Ramsey theory and Higman's lemma
We present a short and elementary proof of the Ajtai-Koml\'os-Tusn\'ady (AKT) optimal matching theorem in dimension 2 via Fourier analysis and a smoothing argument. The upper bound applies to more general families of samples, including…
In this article we present the history of auxiliary primes used in proofs of reciprocity laws from the quadratic to Artin's reciprocity law. We also show that the gap in Legendre's proof can be closed with a simple application of Gauss's…
Watson proved Kirkman's hypothesis (partially solved by Cayley). Using Lagrange Inversion, we drastically shorten Watson's computations and generalize his results at the same time.
Using various results from extremal set theory (interpreted in the language of additive combinatorics), we prove an asyptotically sharp version of Freiman's theorem in F_2^n: if A in F_2^n is a set for which |A + A| <= K|A| then A is…
We prove a sharp structural result concerning finite colorings of pairs in well-founded trees.
In this thesis, we investigate the computational content and the logical strength of Ramsey's theorem and its consequences. For this, we use the frameworks of reverse mathematics and of computable reducibility. We proceed to a systematic…
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We characterize the strength, in terms of Weihrauch degrees, of certain problems related to Ramsey-like theorems concerning colourings of the rationals and of the natural numbers. The theorems we are chiefly interested in assert the…
An approach to constructing an upper bound for the Riemann-Farey sum is described.
We give an exponential improvement to the lower bound on diagonal Ramsey numbers for any fixed number of colors greater than two.
In recent years, there has been a substantial amount of work in reverse mathematics concerning natural mathematical principles that are provable from $\RT$, Ramsey's Theorem for Pairs. These principles tend to fall outside of the "big five"…
We prove tight bounds for the $\infty$-norm of the inverse of symmetric, diagonally dominant positive matrices. We also prove a new lower-bound form of Hadamard's inequality for the determinant of diagonally dominant positive matrices and…
We present an exposition of the proof of the induced bipartite Ramsey Theorem.
The paper presents a counterexample to the Hodge conjecture.
The main purpose of this note is to prove an upper bound on the number of lattice points of a centrally symmetric convex body in terms of the successive minima of the body. This bound improves on former bounds and narrows the gap towards a…
In this paper, we give a comparison version of Pythagorean Theorem to judge the lower or upper bound of the curvature of Alexandrov spaces (including Riemannian manifolds).
In this paper we give a new proof of Riemann's well known mapping theorem. The suggested method permits to prove an analog of that theorem for the three dimensional case.
We define a collection of topological Ramsey spaces consisting of equivalence relations on $\omega$ with the property that the minimal representatives of the equivalence classes alternate according to a fixed partition of $\omega$. To prove…
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…
A local strict comparison theorem and some converse comparison theorems are proved for reflected backward stochastic differential equations under suitable conditions.