195 research outputs found
Overpartition pairs and two classes of basic hypergeometric series
We study the combinatorics of two classes of basic hypergeometric series. We
first show that these series are the generating functions for certain
overpartition pairs defined by frequency conditions on the parts. We then show
that when specialized these series are also the generating functions for
overpartition pairs with bounded successive ranks, overpartition pairs with
conditions on their Durfee dissection, as well as certain lattice paths. When
further specialized, the series become infinite products, leading to numerous
identities for partitions, overpartitions, and overpartition pairs.Comment: 31 pages, To appear in Adv. Mat
Duality and quantum-algebra symmetry of the A_{N-1}^(1) open spin chain with diagonal boundary fields
We show that the transfer matrix of the A_{N-1}^(1) open spin chain with
diagonal boundary fields has the symmetry U_q (SU(L)) x U_q (SU(N-L)) x U(1),
as well as a ``duality'' symmetry which interchanges L and N - L. We exploit
these symmetries to compute exact boundary S matrices in the regime with q
real.Comment: 27 pages, LaTeX, 1 LaTeX figur
Classical Scattering in Dimensional String Theory
We find the general solution to Polchinski's classical scattering equations
for dimensional string theory. This allows efficient computation of
scattering amplitudes in the standard Liouville background.
Moreover, the solution leads to a mapping from a large class of time-dependent
collective field theory backgrounds to corresponding nonlinear sigma models.
Finally, we derive recursion relations between tachyon amplitudes. These may be
summarized by an infinite set of nonlinear PDE's for the partition function in
an arbitrary time-dependent background.Comment: 15 p
Algorithms Seminar, 2002-2004
These seminar notes constitute the proceedings of a seminar devoted to the analysis of algorithms and related topics. The subjects covered include combinatorics, symbolic computation, and the asymptotic analysis of algorithms, data structures, and network protocols
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