arXiv subjects

B. S. Kochkarev

Publications and source records attributed to B. S. Kochkarev.

4 recordsLinked to original sources

arXiv2013

Typical property of one class of combinatory objects and estimation from above corresponding combinatory numbers

We investigate properties of families $F$ of subsets of a finite set in a situation where subsets are incomparable by the binary inclusion relation and a) for any $A\notin F$, there is such set $A'\in F$ that either $A\subset A'$ or $A'\subset A$; b) for any $A\in F$, $\mid A\mid\in \{k,k+1\}$. For these families we introduce one parametre and we show that for almost all families $F$ the value of this parametre is ${n-1\choose k}$. We show that families with the minimum value of the entered parametre have certain structure and we find also number of such families. At last, we find an estimation from above for combinatory numbers of considered combinatory objects.

cs.DM↗

arXiv2013

Proof of the hypothesis Edmonds's, not polynomial of NPC-problems and classification of the problems with polynomial certificates

We show that the affirmation $P\subseteq NP$ (in computer science) erroneously and we prove the justice of the hypotesis J.Edmonds's $P\neq NP$. We show further that all the $NP$-complete problems is not polynomial and we give the classification of the problems with the polynomial certificates.

cs.CC↗

arXiv2012

About one class polynomial problems with not polynomial certificates

We build a class of polynomial problems with not polynomial certificates. The parameter concerning which are defined efficiency of corresponding algorithms is the number $n$ of elements of the set has used at construction of combinatory objects (families of subsets) with necessary properties.

math.GM↗

arXiv2012

Absolutely symmetric trees and complexity of natural number

We consider the rooted trees which not have isomorphic representation and introduce a conception of complexity a natural number also. The connection between quantity such trees with $n$ edges and a complexity of natural number $n$ is established. The recurrent ratio for complexity of a natural number is founded. An expression for calculation of difference complexities of two adjacent natural numbers is constructed. It is proved that this difference equal 1 if and only if a natural number is simple. From proved theorems it follows corollaries.

math.CO↗