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Vladimir Blinovsky

Publications and source records attributed to Vladimir Blinovsky.

At least 19 recordsLinked to original sources
arXiv2025

Erdös's Matching Conjecture and $s$-wise $t$-intersection Conjecture via Symmetrical Smoothing Method

We find the formula for the maximal cardinality of the family of $n$-tuples from ${[n]\choose k}$ with does not have $\ell$--matching. This formula after some analytical issues can be reduce to the Erdös's Matching formula. Also we prove the conjecture about the cardinality of maximal $s$-wise $t$-intersecting family of $k$-element subsets of $[n]$. In the proofs we use original method which we have already used in the proof of Miklós-Manikam-Singhi conjecture in \cite{1}. We call this method Symmetrical smoothing method, we add small corrections

math.CO↗
arXiv2017

Proof of Riemann hypothesis

We prove Riemann hypothesis. Method is to show the convexity of function which has zeros on open critical strip the same as zeta function.

math.GM↗
arXiv2017

Comments to Symmetrical Smoothing Method and First Step to How to Avoid Irrelevant Extremums

The main issues of the original Symmetrical smoothing method consists of approximation of the extremal volume of the set by the smooth symmetric function (sum of step functions) and then solve the optimization problem. when making optimization, besides symmetric solution, can occur another pretendents for the solution, which depends on $σ$. Next we show simple way how to avoid them.

math.CO↗
arXiv2016

Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees

A hypergraph is simple if it has no loops and no repeated edges, and a hypergraph is linear if it is simple and each pair of edges intersects in at most one vertex. For $n\geq 3$, let $r= r(n)\geq 3$ be an integer and let $\boldsymbol{k} = (k_1,\ldots, k_n)$ be a vector of nonnegative integers, where each $k_j = k_j(n)$ may depend on $n$. Let $M = M(n) = \sum_{j=1}^n k_j$ for all $n\geq 3$, and define the set $\mathcal{I} = \{ n\geq 3 \mid r(n) \text{ divides } M(n)\}$. We assume that $\mathcal{I}$ is infinite, and perform asymptotics as $n$ tends to infinity along $\mathcal{I}$. Our main result is an asymptotic enumeration formula for linear $r$-uniform hypergraphs with degree sequence $\boldsymbol{k}$. This formula holds whenever the maximum degree $k_{\max}$ satisfies $r^4 k_{\max}^4(k_{\max} + r) = o(M)$. Our approach is to work with the incidence matrix of a hypergraph, interpreted as the biadjacency matrix of a bipartite graph, enabling us to apply known enumeration results for bipartite graphs. This approach also leads to a new asymptotic enumeration formula for simple uniform hypergraphs with specified degrees, and a result regarding the girth of random bipartite graphs with specified degrees.

math.CO↗
arXiv2015

Asymptotic enumeration of sparse uniform hypergraphs with given degrees

Let $r \geq 2$ be a fixed integer. For infinitely many $n$, let $\boldsymbol{k} = (k_1,..., k_n)$ be a vector of nonnegative integers such that their sum $M$ is divisible by $r$. We present an asymptotic enumeration formula for simple $r$-uniform hypergraphs with degree sequence $k$. (Here "simple" means that all edges are distinct and no edge contains a repeated vertex.) Our formula holds whenever the maximum degree $k_{\mathrm{max}}$ satisfies $k_{\mathrm{max}}^3 = o(M)$.

math.CO↗
arXiv2015

Fractional matching in hypergraphs

We find the exact formula for the minimal number of edges of hypergraph which guaranteed fractional matching of cardinality $s$ in the case when $sn$ is integer.

math.CO↗