Lev Glebsky
Balanced $0,1$-words and the Galois group of $(x+1)^n-\lambda x^p$.
Tue, 11/15/2011 - 15:01 — SomNambulAuthors: Lev Glebsky
Subjects: Combinatorics
AbstractWe study the number of $0,1$-words where the fraction of 0 is "almost" fixed
for any initial subword. It turns out that this study use and reveal the
structure of the Galois group (the monodromy group) of the polynomials
$(x+1)^n-\lambda x^p$. ($p$ is not necessary a prime here.)Almost commuting matrices with respect to normalized Hilbert-Schmidt norm.
Wed, 02/17/2010 - 16:01 — SomNambulAuthors: Lev Glebsky
Subjects: Algebraic Geometry
AbstractAlmost-commuting matrices with respect to the normalized Hilbert-Schmidt norm
are considered. Normal almost commuting matrices are proved to be near
commuting.Short Cycles in Repeated Exponentiation Modulo a Prime.
Fri, 08/28/2009 - 23:56 — SomNambulAuthors: Lev Glebsky, Igor E. Shparlinski
Subjects: Number Theory
AbstractGiven a prime $p$, we consider the dynamical system generated by repeated
exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where
$f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le p-1$. This map is in
particular used in a number of constructions of cryptographically secure
pseudorandom generators. We obtain nontrivial upper bounds on the number of
fixed points and short cycles in the above dynamical system.
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