Related papers: On the infinitary van der Waerden Theorem
We prove the constructive version of Birkhoff's ergodic theorem following Vyugin but trying to separate and state explicitly the combinatorial statement on which this proof is based. We pose some questions related to this statement (and the…
We prove the Complete nontrivial cycle-intersection theorem for systems of permutations.
We give a simple proof of Dorronsoro's theorem and use similar ideas to establish an equivalence for embeddings of vector fields.
Pirillo and Varricchio, and independently, Halbeisen and Hungerbuhler considered the following problem, open since 1994: Does there exist an infinite word w over a finite subset of Z such that w contains no two consecutive blocks of the…
In this paper we review a general proof for the irrationality property of numbers which take a certain form of infinite sums.
Simple argument in favour of unitarity, to all orders, of space-like noncommutative theory is given.
We prove the Aharoni Berger Conjecture
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
A proof is given of Rosenthal's \(\ell_1\) theorem.
We propose a combinatorial interpretation of the coefficient of $q$ in Kazhdan- Lusztig polynomials and we prove it for finite simply-laced Weyl groups.
We will describe a combinatorial game that models the problem of resolution of singularities of algebraic varieties over a field of characteristic zero. By giving a winning strategy for this game, we give another proof of the existence of…
In this note we use the monodromy argument to prove a Noether-Lefschetz theorem for vector bundles.
In this short note, we prove Hadwiger's conjecture for strongly monotypic polytopes.
We give a short, explicit proof of Hindman's Theorem that in every finite coloring of the integers, there is an infinite set all of whose finite sums have the same color. We give several exampls of colorings of the integers which do not…
A very simple but useful almost sure convergence theorem of probability is given.
Let $T$ be a countable complete first-order theory with a definable, infinite, discrete linear order. We prove that $T$ has continuum-many countable models. The proof is purely first-order, but raises the question of Borel completeness of…
In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…
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.
We provide a self-contained proof of the Artin-Wedderburn theorem in the case of finite-dimensional Von Neumann algebras (or equivalently unital C* algebras) that is fully constructive and uses only basic notions of linear algebra.