Related papers: A Counting Proof of the Graham Pollak Theorem

We prove a variation of Gronwall's lemma.

We present a method for constructing countable models of small theories and apply it to prove theorems on the maximal number of countable non-isomorphic models of linearly ordered theories.

We find an elementary proof for Voiculescu's theorem on the polar decomposition of circular variables.

In this paper we review a general proof for the irrationality property of numbers which take a certain form of infinite sums.

An technically interesting proof of a known theorem.

This paper presents a short and simple proof of the Four-Color Theorem that can be utterly checkable by human mathematicians, without computer assistance. The new key idea that has allowed it and the global structure of the proof are…

We give a direct geometric proof of the quantum Monk's formula which relies only on classical Schubert calculus.

We present a short, elementary proof not involving Fourier transforms of the theorem of Cram\'er and Wold that a Borel probability measure is determined by its values on half-spaces.

We prove Union-Closed sets conjecture.

We give a q-analogue of Gauss' divisibility theorem

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

General acceptance of a mathematical proposition $P$ as a theorem requires convincing evidence that a proof of $P$ exists. But what constitutes "convincing evidence?" I will argue that, given the types of evidence that are currently…

We sketch several proofs of F\'ary--Milnor theorem.

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

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.

A vector variational principle is proved.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We present a sequent-style proof system for provability logic GL that admits so-called circular proofs. For these proofs, the graph underlying a proof is not a finite tree but is allowed to contain cycles. As an application, we establish…

In the first section of this paper we prove a theorem for the number of columns of a rectangular area that are identical to the given one. In the next section we apply this theorem to derive several combinatorial identities by counting…

Extending the idea in [Impagliazzo, R., Moore, C. and Russell, A., An entropic proof of Chang's inequality. SIAM Journal on Discrete Mathematics, 28(1), pp.173-176.] we give a short information theoretic proof for Chang's lemma that is…