Related papers: Short proof of the Gallai-Edmonds Structure Theore…

In this paper we extend To\"en's derived Hall algebra construction, in which he obtains unital associative algebras from certain stable model categories, to one in which such algebras are obtained from more general stable homotopy theories,…

We prove that a strengthened form of the local Langlands conjecture is valid throughout the principal series of any connected split reductive $p$-adic group. The method of proof is to establish the presence of a very simple geometric…

We present a short and self-contained proof of the choosability version of Brooks' theorem.

Based on M. Hall's theorem we prove a simple result dealing with real numbers which admit exact approximations by rationals.

We introduce a geometric generalization of Hall's marriage theorem. For any family $F = \{X_1, \dots, X_m\}$ of finite sets in $\mathbb{R}^d$, we give conditions under which it is possible to choose a point $x_i\in X_i$ for every $1\leq i…

This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…

We give a short proof of a strengthening of the Maximal Ergodic Theorem which also immediately yields the Pointwise Ergodic Theorem.

In this note we define a generalization of Hall-Littlewood symmetric functions using formal group law and give an elementary proof of the generating function formula for the generalized Hall-Littlewood symmetric functions. We also give some…

In this paper, we study shape functions depending on closed submanifolds. We prove a new structure theorem that establishes the general structure of the shape derivative for this type of shape function. As a special case we obtain the…

We give a new simpler proof of a theorem of Jayne and Rogers.

We give a constructive proof of Carpenter's Theorem due to Kadison. Unlike the original proof our approach also yields the real case of this theorem.

The Bollob\'as-Varopoulos theorem is an analogue of Hall's matching theorem on non-atomic measure spaces. Here we prove a finite version with a completely constructive proof.

Simple and shorter proofs of two Dirac-type theorems involving connectivity are presented.

We give a q-analogue of Gauss' divisibility theorem

We give a purely combinatorial proof of the density Hales--Jewett Theorem that is modeled after Polymath's proof but is significantly simpler. In particular, we avoid the use of the equal-slices measure and work exclusively with the uniform…

I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.

We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].

The Erd\H{o}s-Gallai Theorem states that every graph of average degree more than $l-2$ contains a path of order $l$ for $l\ge 2$. In this paper, we obtain a stability version of the Erd\H{o}s-Gallai Theorem in terms of minimum degree. Let…

We give a short proof of a theorem of J.-E. Pin (theorem 1.1 below), which can be found in his thesis. The part of the proof which is my own (not Pin's) is a complete replacement of the same part in an earlier version of this paper.

We show that Isserlis' theorem follows as a corollary to the invariant tensor theorem for isotropic tensors.