Carlos Vinuesa
Generalization of a theorem of Erdos and Renyi on Sidon Sequences.
Tue, 11/17/2009 - 16:01 — SomNambulAuthors: Carlos Vinuesa, Javier Cilleruelo, Imre Z. Ruzsa, Sandor Z. Kiss
Subjects: Number Theory
AbstractErd\H os and R\'{e}nyi claimed and Vu proved that for all $h \ge 2$ and for
all $\epsilon > 0$, there exists $g = g_h(\epsilon)$ and a sequence of integers
$A$ such that the number of ordered representations of any number as a sum of
$h$ elements of $A$ is bounded by $g$, and such that $|A \cap [1,x]| \gg x^{1/h
- \epsilon}$.Generalized Sidon sets.
Tue, 09/29/2009 - 15:21 — SomNambulAuthors: Carlos Vinuesa, Javier Cilleruelo, Imre Z. Ruzsa
Subjects: Combinatorics
AbstractWe give asymptotic sharp estimates for the cardinality of a set of residue
classes with the property that the representation function is bounded by a
prescribed number. We then use this to obtain an analogous result for sets of
integers, answering an old question of Simon Sidon.Improved bounds on the supremum of autoconvolutions.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Mate Matolcsi, Carlos Vinuesa
Subjects: Classical Analysis and ODEs
AbstractWe give a slight improvement of the best known lower bound for the supremum
of autoconvolutions of nonnegative functions supported in a compact interval.
Also, by means of explicit examples we disprove a long standing natural
conjecture of Schinzel and Schmidt concerning the extremal function for such
autoconvolutions.Improved bounds on the supremum of autoconvolutions.
Mon, 09/07/2009 - 10:33 — SomNambulAuthors: Mate Matolcsi, Carlos Vinuesa
Subjects: Classical Analysis and ODEs
AbstractWe give a slight improvement of the best known lower bound for the supremum
of autoconvolutions of nonnegative functions supported in a compact interval.
Also, by means of explicit examples we disprove a long standing natural
conjecture of Schinzel and Schmidt concerning the extremal function for such
autoconvolutions.
User login
