Related papers: A Counting Proof of the Graham Pollak Theorem

In this paper I present a kind of proof for classical Euclidean geometric problems which relies on both synthetic and analytic geometry. Using the elementary tools of polynomial algebra and multivariate calculus we manage to reduce the…

Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.

We present in this work a new and simple proof of the false centre theorem.

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

We provide a proof of a variant of the Landau-Siegel Zeros conjecture.

Using the correspondence between a cycle up-down permutation and a pair of matchings, we give a combinatorial proof of the enumeration of alternating permutations according to the given peak set.

This note contains a new combinatorial proof of Cramer's rule based on the Gessel-Viennot-Lindstrom Lemma.

We present an easy proof of Polya's theorem on random walks: with the probability one a random walk on the two-dimensional lattice returns to the starting point.

Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.

We consider the problem of counting the number of answers to a first-order formula on a finite structure. We present and study an extension of first-order logic in which algorithms for this counting problem can be naturally and conveniently…

In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.

We study counting propositional logic as an extension of propositional logic with counting quantifiers. We prove that the complexity of the underlying decision problem perfectly matches the appropriate level of Wagner's counting hierarchy,…

In this note, we present a simple non-directed graph proof of Sharkovsky's theorem which is different from the one given in [2].

This note concerns a one-line diagrammatic proof of the Cayley-Hamilton Theorem. We discuss the proof's implications regarding the "core truth" of the theorem, and provide a generalization. We review the notation of trace diagrams and…

The main result is that for lambda strong limit singular failing the continuum hypothesis (i.e. 2^lambda > lambda^+), a polarized partition theorem holds.

We provide a simple proof of Tchakaloff's Theorem on the existence of cubature formulas of degree $m$ for Borel measures with moments up to order $m$. The result improves known results for non-compact supports, since we do not need…

We provide a proof of the Borwein Conjecture using analytic methods.

We prove analogues of the Craig interpolation theorem for the continuous model theory of metric structures.

In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…

We prove the abundance theorem for numerically trivial log canonical divisors of log canonical pairs and semi-log canonical pairs.