Related papers: New 5-designs---revisited

The main aim of this work is to present an explicit construction of a 2-design of ${\rm U}(2)$, relying only on a tool that belongs to every physicists toolbox: the theory of angular momentum. Unitary designs are a rich and fundamental…

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

We revisit Bressoud's generalized Borwein conjecture. Making use of new positivity-preserving transformations for q-binomial coefficients we establish the truth of infinitely many cases of the Bressoud conjecture. In addition, we prove new…

A simple proof of the celebrated theorem of Lee and Yang is attempted in this short note.

Fifth order exact corrections to the non-singlet electron structure function in QED are the leading logarithmic approximation using the ad hoc exponentiation prescription proposed by Jadach and Ward and a recurence formula for the elements…

In this paper, the easier methods of my thesis are applied to give a simple proof of a theorem of Goussarov. The theorem relates two possible notions of finite type equivalence of knots, links or string links, showing that the resulting…

The main results in this note concern the characterization of the length of continua 1 (Theorems 2.5) and the parametrization of continua with finite length (Theorem 4.4). Using these results we give two independent and relatively…

We give estimates on the number of combinatorial designs, which prove (and generalise) a conjecture of Wilson from 1974 on the number of Steiner Triple Systems. This paper also serves as an expository treatment of our recently developed…

We survey the classical results on the prime number theorem

In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…

A Gleason-type theorem is proved for two restricted classes of informationally complete POVMs in the qubit case. A particular (incomplete) Kochen-Specker colouring, suggested by Appleby in dimension three, is generalized to arbitrary…

Here I give a description of Alexandrov 4-point comparison via quadratic forms and then propose a natural 5-point condition which might have some future. Consider this note as a letter from me --- do not take it seriously.

In this note we show that McGee's {\omega}-inconsistency result can be derived from L\"ob's theorem.

We give new proofs of some well-known results from Invariant Theorey using the Kempf-Ness theorem.

We prove an identity for Littlewood--Richardson coefficients conjectured by Pelletier and Ressayre (arXiv:2005.09877). The proof relies on a novel birational involution defined over any semifield.

These notes are designed to offer some (perhaps new) codicils to related work, a list of problems and conjectures seeking (preferably) combinatorial proofs. The main items are Eulerian polynomials and hook/contents of Young diagram, mostly…

Question when rectangle can be tiled with similar copies of rectangles witch quetient of sides quadratic irrationalities. New proof of one part F. Sharov's theorem. Other close result.

We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirror symmetry. We also prove homological mirror symmetry for…

In this short note, we give a new proof of a theorem of Arezzo-Tian on the existence of smooth geodesic rays tamed by a special degeneration.

We discuss the method recently proposed by S. Chubanov for the linear feasibility problem. We present new, concise proofs and interpretations of some of his results. We then show how our proofs can be used to find strongly polynomial time…