Related papers: A proof of the Graham Sloane conjecture

In this paper, we obtained an equivalent proposition of Brennan`s conjecture. And given two lower bound estimation of the conjecture one of them connected with Schwarzian derivative. The present study also verified the correctness of the…

We survey most of the known results concerning the Eisenbud-Green-Harris Conjecture. Our presentation includes new proofs of several theorems, as well as a unified treatment of many results which are otherwise scattered in the literature.…

We prove The Tate Thomason conjecture through Theorem 2.2. Fundamental is the work of R W Thomson and the proof also rests upon the theory of infinite abelian groups.

We prove a result on the existence of linear forms of a given Diophantine type.

We show that Generic Green's conjecture holds for generic binary curves, through a detailed analysis of the family of scrolls containing fixed rational normal curves.

A combinatorial proof of the Gordon Conjecture: The sum of two Heegaard splittings is stabilized if and only if one of the two summands is stabilized.

We consider the immediate consequence of an arguable addition to the standard Deduction Theorems of first order theories.

We present an exposition of the proof of the induced bipartite Ramsey Theorem.

We prove some new results related to Tanaka's formula.

In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.

We prove that a contractible orbifold is a manifold.

Foulkes' conjecture has several generalisations due to Doran, Abdesselam--Chipalkatti, Bergeron, and Troyka. For the special linear Lie algebra $\mathfrak{sl}_2(\mathbb{C})$, these assert that given $a \le c \le d \le b$ with $ab=cd$, the…

New cases of the multiplicity conjecture are considered.

We prove a connectedness result for products of weighted projective spaces.

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

We outline a proof of the categorical geometric Langlands conjecture for GL(2), as formulated in reference [AG], modulo a number of more tractable statements that we call Quasi-Theorems.

We expose here a short proof of Cramer's theorem in R based on convex duality.

We prove a dualization of the Graham--Rothschild Theorem for variable words indexed by homogeneous trees.

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.

We prove an analogue of the fixed-point theorem for the case of definably amenable groups.