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pro vyhledávání: '"Lerner, E. Yu."'
Autor:
Lerner, E. Yu.
Given a simple biconnected planar cubic graph, we associate each its vertex among $2n$ ones with the so-called spin, i.e., a variable which takes on values $\pm 1$. P. J. Heawood has proved that a Tait coloring, accurate to the choice of a color for
Externí odkaz:
http://arxiv.org/abs/2411.15992
Autor:
Lerner, E. Yu.
In 1977, Yu. V. Matiyasevich proposed a formula expressing the chromatic polynomial of an arbitrary graph as a linear combination of flow polynomials of subgraphs of the original graph. In this paper, we prove that this representation is a particular
Externí odkaz:
http://arxiv.org/abs/2404.09347
Autor:
Lerner, E. Yu
Given $n$ men, $n$ women, and $n$ dogs, we assume that each man has a complete preference list of women, while each woman does a complete preference list of dogs, and each dog does a complete preference list of men. We study the so-called 3D-CYC prob
Externí odkaz:
http://arxiv.org/abs/2107.10102
Autor:
Lerner, E. Yu., Lerner, R. E.
Given $n$ men, $n$ women, and $n$ dogs, each man has an incomplete preference list of women, each woman does an incomplete preference list of dogs, and each dog does an incomplete preference list of men. We understand a family as a triple consisting
Externí odkaz:
http://arxiv.org/abs/2101.08223
Autor:
Bochkarev, V. V., Lerner, E. Yu.
Publikováno v:
Russian Mathematics. 2012, Volume 56, Issue 12, pp 25-27
We model the generation of words with independent unequal probabilities of occurrence of letters. We prove that the probability $p(r)$ of occurrence of words of rank $r$ has a power asymptotics. As distinct from the paper published earlier by B. Conr
Externí odkaz:
http://arxiv.org/abs/1205.0796
Autor:
Lerner, E. Yu.
Publikováno v:
Functional Analysis and Other Mathematics, Springer Berlin / Heidelberg, Vol. 3, Issue 1 (2010), pp 75-83
In this paper we answer certain questions posed by V.I. Arnold, namely, we study periods of continued fractions for solutions of quadratic equations in the form $x^2+p x=q$ with integer $p$ and $q$, $p^2+q^2\le R^2$. Our results concern the average s
Externí odkaz:
http://arxiv.org/abs/0904.0616
Autor:
Lerner, E. Yu.
V.I. Arnold has experimentally established that the limit of the statistics of incomplete quotients of partial continued fractions of quadratic irrationalities coincides with the Gauss--Kuz'min statistics. Below we briefly prove this fact for roots o
Externí odkaz:
http://arxiv.org/abs/0810.0718
Autor:
Lerner, E. Yu
Publikováno v:
Functional Analysis and Other Mathematics, Springer Berlin / Heidelberg, Vol. 2, Issues 2-4, 2009, pp 251-255
V.I. Arnold has recently defined the complexity of a sequence of $n$ zeros and ones with the help of the operator of finite differences. In this paper we describe the results obtained for almost most complicated sequences of elements of a finite fiel
Externí odkaz:
http://arxiv.org/abs/0710.3451
Autor:
Lerner, E. Yu.
V.I. Arnold has recently defined the complexity of finite sequences of zeroes and ones in terms of periods and preperiods of attractors of a dynamic system of the operator of finite differentiation. Arnold has set up a hypothesis that the sequence of
Externí odkaz:
http://arxiv.org/abs/0710.2088
Autor:
Lerner, E. Yu.
Let $x$ be a cyclic sequence of $n$ elements of the finite field $\mathbb{F}_q$ (the first element immediately follows the $n$-th one). Let us define the operation $\Delta$ as the transition from $x$ to the sequence of differences of the neighbouring
Externí odkaz:
http://arxiv.org/abs/0704.2947