Related papers: Proof of the orthogonal--Pin duality

In this note we fill a gap in the proof of the main theorem (Theorem 1.2) of our paper 'Surfaces in 4-manifolds', Math. Res. Letters 4 (1997), 907-914.

Several cases of Fock space duality occurring in the theory of many-body systems in general and nuclei in particular are discussed. All of them are special cases of a general duality theorem proved in mathematics by Howe in the 1970s.…

An O(n) test for polygon convexity is stated and proved. It is also proved that the test is minimal in a certain exact sense.

In this paper we consider Erd\"os-Mordell inequality and its extension in the plane of triangle to the Erd\"os-Mordell curve. Algebraic equation of this curve is derived, and using modern computer tools in mathematics, we verified one…

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…

An technically interesting proof of a known theorem.

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

In this article we prove that for a large class of 2-dimensional minimal cones (including almost all 2-dimensional minimal cones that we know), the almost orthogonal union of any two of them is still a minimal cone. Comparing to existing…

This is an example on the cohomology of threefolds.

A vector variational principle is proved.

We will present a new proof of the Gromoll-Grove diameter rigidity theorem.

I expound here in a more detailed way a proof of an important Serini's theorem, which I have already sketched in a previous Note. Two related questions are briefly discussed.

The paper provides an elementary proof of Kenyon's necessary condition for the existence of a periodic tiling of the plane by squares with given periods. A similar new result on covering both sides of a rectangle by nonoverlaping squares is…

I have withdrawn the paper, after having incorporated it into the paper arXiv:0712.3484. In the meantime I have discovered that one of the theorems proved in the paper had already been proved by Durfee & Hain.

Torelli's theorem is proven by the study of the convolution product of the intersection cohomology sheaf of the thetadivisor.

Weighted enumeration of reduced pipe dreams (or rc-graphs) results in a combinatorial expression for Schubert polynomials. The duality between the set of reduced pipe dreams and certain antidiagonals has important geometric implications [A.…

Specker's principle, the condition that pairwise orthogonal propositions must be jointly orthogonal, has been much investigated recently within the programme of finding physical principles to characterise quantum mechanics. It largely…

In this article we prove some theorems related to the triplets of triangles, homological two by two. These theorems will be used later to build triplets of triangles two by two tri-homological.

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

We show that there is a strong minimal pair in the computably enumerable Turing degrees.