14,891 research outputs found
A lower bound for the -multicolored sum-free problem in
In this paper, we give a lower bound for the maximum size of a -colored
sum-free set in , where and are fixed and
tends to infinity. If is a prime power, this lower bound matches (up to
lower order terms) the previously known upper bound for the maximum size of a
-colored sum-free set in . This generalizes a result of
Kleinberg-Sawin-Speyer for the case and as part of our proof we also
generalize a result by Pebody that was used in the work of
Kleinberg-Sawin-Speyer. Both of these generalizations require several key new
ideas
Notes of the Origin of Bony Armor
Paper by H. J. Sawin, Visiting Lecturer in Geolog
Direct Sum Decompositions and Indecomposable TQFT's
The decomposition of an arbitrary axiomatic topological quantum field theory
or TQFT into indecomposable theories is given. In particular, unitary TQFT's in
arbitrary dimensions are shown to decompose into a sum of theories in which the
Hilbert space of the sphere is one-dimensional, and indecomposable
two-dimensional theories are classified.Comment: 10 pages, AMSLaTeX, 5 figures compressed and uuencoded by uufile
Path Integration in Two-Dimensional Toplogical Quantum Field Theory
A positive, diffeomorphism-invariant generalized measure on the space of
metrics of a two-dimensional smooth manifold is constructed. We use the term
generalized measure analogously with the generalized measures of Ashtekar and
Lewandowski and of Baez. A family of actions is presented which, when
integrated against this measure, give the two-dimensional axiomatic topological
quantum field theories, or TQFT's, in terms of which Durhuus and Jonsson
decompose every two-dimensional unitary TQFT as a direct sum.Comment: 13 pages, LaTeX with amsfonts and psfig, 3 postscript figures and
.bbl file tar'd and compressed by uufile
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