Related papers: A Counting Proof of the Graham Pollak Theorem
We give a procedure for counting the number of different proofs of a formula in various sorts of propositional logic. This number is either an integer (that may be 0 if the formula is not provable) or infinite.
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.
We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.
We survey the classical results on the prime number theorem
We give a proof of the Marker-Steinhorn Theorem which fills a gap in previous proofs of the result.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
We prove a generalization of Lopes's theorem, that is, of the converse of Brolin's theorem.
We prove the theorems which are equivalent to the Roland's results such that a new form of them allows to consider some generalizations. In particular, we give generators of primes more than a fixed prime.
A proof of the continuous martingale convergence theorem is provided. It relies on a classical martingale inequality and the almost sure convergence of a uniformly bounded non-negative super-martingale, after a truncation argument.
We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena
We study the group of ends of a pro-p group G and prove a pro-p analog of Stallings' decomposition theorem.
We give a proof of a Martingale Representation Theorem using the methods of nonstandard analysis.
We illustrate the concept of mathematical proof.
We give a short proof of the strong law of large numbers based on duality for random walk
In this paper, we prove the number of countable models of a countable supersimple theory is either 1 or infinite. This result is an extension of Lachlan's theorem on a superstable theory.
We improve on Gonek-Montgomery's quantitative version of Kronecker's approximation theorem.
This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.
Cook's theorem is commonly expressed such as any polynomial time-verifiable problem can be reduced to the SAT problem. The proof of Cook's theorem consists in constructing a propositional formula A(w) to simulate a computation of TM, and…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.