13,826 research outputs found
On a combinatorial problem of Erdos, Kleitman and Lemke
In this paper, we study a combinatorial problem originating in the following
conjecture of Erdos and Lemke: given any sequence of n divisors of n,
repetitions being allowed, there exists a subsequence the elements of which are
summing to n. This conjecture was proved by Kleitman and Lemke, who then
extended the original question to a problem on a zero-sum invariant in the
framework of finite Abelian groups. Building among others on earlier works by
Alon and Dubiner and by the author, our main theorem gives a new upper bound
for this invariant in the general case, and provides its right order of
magnitude.Comment: 15 page
Strings from Logic
What are strings made of? The possibility is discussed that strings are
purely mathematical objects, made of logical axioms. More precisely, proofs in
simple logical calculi are represented by graphs that can be interpreted as the
Feynman diagrams of certain large-N field theories. Each vertex represents an
axiom. Strings arise, because these large-N theories are dual to string
theories. These ``logical quantum field theories'' map theorems into the space
of functions of two parameters: N and the coupling constant. Undecidable
theorems might be related to nonperturbative field theory effects.Comment: Talk, 19 pp, 7 figure
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