Related papers: Constructive proof of the Carpenter's Theorem
We present an alternative proof of Perron's theorem, which is probabilistic in nature. It rests on the representation of the Perron eigenvector as a functional of the trajectory of an auxiliary Markov chain.
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
We give a new simpler proof of a theorem of Jayne and Rogers.
In this note we shall give a new proof to a quadrature formulae due to Newton.
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
Constructivists (and intuitionists in general) asked what kind of mental construction is needed to convince ourselves (and others) that some mathematical statement is true. This question has a much more practical (and even cynical)…
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
We discuss the proof of a certain integral theorem obtained by C. G. Cullen, originally stated on the class of the analytic intrinsic functions on the quaternions. It is shown that this integral theorem is true for a larger class of…
In this paper we give a new proof of the Ne\v{s}et\v{r}il-R\"odl Theorem, a deep result of discrete mathematics which is one of the cornerstones of the structural Ramsey theory. In contrast to the well-known proofs which employ intricate…
In this note we exhibit a very simple proof of McNaughton Theorem, almost right out of the definitions, and at the same time we observe that this theorem does not depend of Chang's completeness theorem.
This is the second combinatorial proof of the compactness theorem for singular from 1977. In fact it gives a somewhat stronger theorem.
In this paper we give a mathematical proof of Dodgson algorithm [1]. Recently Zeilberger [2] gave a bijective proof. Our techniques are based on determinant properties and they are obtained by induction.
Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery such as ultrafilters, nets or maximal families with the finite intersection property are employed to give proofs that can be very neat, but not the kind of thing…
We give a purely combinatorial proof of the Glaisher-Crofton identity which derives from the analysis of discrete structures generated by iterated second derivative. The argument illustrates utility of symbolic and generating function…
This paper is meant to be a gentle introduction to Carleson's Theorem on pointwise convergence of Fourier series.
We provide a combinatorial proof of an infinite extension of the Hales--Jewett theorem due to T. Carlson and independently due to H. Furstenberg and Y. Katznelson
We give a purely combinatorial proof for the infinitary van der Waerden's theorem.
In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…
Given a II$_1$ factor M and a masa A of M, we prove a version of the Schur-Horn Theorem, together with a contractive version. These results are inspired on a recent conjecture of Arveson and Kadison (math.OA/0508482).
We present the theory of higher order invariants and higher order automorphic forms in the simplest case, that of a compact quotient. In this case many things simplify and we are thus able to prove a more precise structure theorem than in…