Related papers: A short proof of Combinatorial Nullstellensatz

In this paper we present a short and elementary proof for the error in Simpson's rule.

In this note, we give an exposition of the construction of Seiberg-Witten invariants.

We present a short and self-contained proof of the extension property for partial isometries of the class of all finite metric spaces.

We provide a short proof of a classical result of Kasteleyn, and prove several variants thereof. One of these results has become key in the parametrization of positroid varieties, and thus deserves the short direct proof which we provide.

We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.

Real Nullstellensatz is a classical result from Real Algebraic Geometry. It has recently been extended to quaternionic polynomials by Alon and Paran. The aim of this paper is to extend their Quaternionic Nullstellensatz to matrix…

We present sharp estimates for the degree and the height of the polynomials in the Nullstellensatz over $\Z$. The result improves previous work of Philippon, Berenstein-Yger and Krick-Pardo. We also present degree and height estimates of…

In this note I go through the `proof' of frequentistic confidence intervals and show what it logically implies concerning the value of a physical quantity given an experimental observation (nothing).

In this note, we present a simpler way to prove the compactness of the closed intervals in simply ordered set with order topology.

One of the variants to proof the generalized Ito-Wentzell's formula is introduced and examined in this paper. The relationship between different representations of the generalized Ito-Wentzell's formula/ is considered.

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some…

We give a counting based proof of the Graham Pollak Theorem

We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…

In this short note, we discuss the Barndorff-Nielsen lemma, which is a generalization of well-known Borel-Cantelli lemma. Although the result stated in the Barndorff-Nielsen lemma is correct, it does not follow from the argument proposed in…

We provide a simple proof of the radial symmetry of any nonnegative minimizer for a general class of quasi-linear minimization problems

We present a proof of Moessner's theorem by double induction, using only basic rules of arithmetic. No prerequisite knowledge is assumed. Familiarity with summation is advised.

We present a short, self-contained, and purely combinatorial proof of Linnik's theorem: for any $\varepsilon > 0$ there exists a constant $C_\varepsilon$ such that for any $N$, there are at most $C_\varepsilon$ primes $p \leqslant N$ such…

In this note we prove a weighted version of the Khintchine inequalities.

We study distribution of zeros of a complex polynomial whose coefficients has been modified. We give a new proof of the theorem of Rubinstein, and with similar method we prove a new theorem that is not generalization of the previous…

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