相关论文: A short proof of the existence of designs

We give a short proof for the existence of the small Witt design which is based on the projective plane of order three with one point deleted.

We produce a new, shorter construction of a minor-universal planar graph.

We prove the existence of subspace designs with any given parameters, provided that the dimension of the underlying space is sufficiently large in terms of the other parameters of the design and satisfies the obvious necessary divisibility…

We give a new simpler proof of a theorem of Jayne and Rogers.

An technically interesting proof of a known theorem.

We provide new families of minimal codes in any characteristic. Also, an inductive construction of minimal codes is presented.

A design is a finite set of points in a space on which every "simple" functions averages to its global mean. Illustrative examples of simple functions are low-degree polynomials on the Euclidean sphere or on the Hamming cube. We prove lower…

In this note, we will give a short proof of an identity for cubic partitions.

Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.

We give a new short proof for the uniqueness of the universal minimal space. The proof holds for the uniqueness of the universal object in every collection of topological dynamical systems closed under taking projective limits and…

We describe the Dedekind cuts explicitly in terms of non-standard rational numbers. This leads to another construction of a Dedekind complete totally ordered field or, equivalently, to another proof of the consistency of the axioms of the…

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

We prove the existence of designs of small size in a number of contexts. In particular our techniques can be applied to prove the existence of $n$-designs on $S^{d}$ of size $O_d(n^{d}\log(n)^{d-1})$.

We describe two distinct simple, short and self contained proofs of the composition lemma.

A novel approach to an old symmetry problem is developed. A new proof is given for the following symmetry problem, studied earlier.

We prove a result on lower bounds in large dimensions.

In this short paper we show that the inequality of arithmetic and geometric means is reduced to another interesting inequality, and a proof is provided.

The purpose of this article is to present my new proof of the the construction and the convergence theorem of spectral sequences of filtered complexes, which is much shorter and cleaner than the "standard" proof.

The $q$-analogs of basic designs are discussed. It is proved that the existence of any unknown Steiner structures, the $q$-analogs of Steiner systems, implies the existence of unknown Steiner systems. Optimal $q$-analogs covering designs…

We prove the existence conjecture for combinatorial designs, answering a question of Steiner from 1853. More generally, we show that the natural divisibility conditions are sufficient for clique decompositions of simplicial complexes that…