82,114 research outputs found
On the enumeration of closures and environments with an application to random generation
Environments and closures are two of the main ingredients of evaluation in
lambda-calculus. A closure is a pair consisting of a lambda-term and an
environment, whereas an environment is a list of lambda-terms assigned to free
variables. In this paper we investigate some dynamic aspects of evaluation in
lambda-calculus considering the quantitative, combinatorial properties of
environments and closures. Focusing on two classes of environments and
closures, namely the so-called plain and closed ones, we consider the problem
of their asymptotic counting and effective random generation. We provide an
asymptotic approximation of the number of both plain environments and closures
of size . Using the associated generating functions, we construct effective
samplers for both classes of combinatorial structures. Finally, we discuss the
related problem of asymptotic counting and random generation of closed
environemnts and closures
Mixed Correlation Functions of the Two-Matrix Model
We compute the correlation functions mixing the powers of two non-commuting
random matrices within the same trace. The angular part of the integration was
partially known in the literature: we pursue the calculation and carry out the
eigenvalue integration reducing the problem to the construction of the
associated biorthogonal polynomials. The generating function of these
correlations becomes then a determinant involving the recursion coefficients of
the biorthogonal polynomials.Comment: 16 page
Extended Rate, more GFUN
We present a software package that guesses formulae for sequences of, for
example, rational numbers or rational functions, given the first few terms. We
implement an algorithm due to Bernhard Beckermann and George Labahn, together
with some enhancements to render our package efficient. Thus we extend and
complement Christian Krattenthaler's program Rate, the parts concerned with
guessing of Bruno Salvy and Paul Zimmermann's GFUN, the univariate case of
Manuel Kauers' Guess.m and Manuel Kauers' and Christoph Koutschan's
qGeneratingFunctions.m.Comment: 26 page
Voting Power of Teams Working Together
Voting power determines the "power" of individuals who cast votes; their
power is based on their ability to influence the winning-ness of a coalition.
Usually each individual acts alone, casting either all or none of their votes
and is equally likely to do either. This paper extends this standard "random
voting" model to allow probabilistic voting, partial voting, and correlated
team voting. We extend the standard Banzhaf metric to account for these cases;
our generalization reduces to the standard metric under "random voting", This
new paradigm allows us to answer questions such as "In the 2013 US Senate, how
much more unified would the Republicans have to be in order to have the same
power as the Democrats in attaining cloture?
Effective Scalar Products for D-finite Symmetric Functions
Many combinatorial generating functions can be expressed as combinations of
symmetric functions, or extracted as sub-series and specializations from such
combinations. Gessel has outlined a large class of symmetric functions for
which the resulting generating functions are D-finite. We extend Gessel's work
by providing algorithms that compute differential equations these generating
functions satisfy in the case they are given as a scalar product of symmetric
functions in Gessel's class. Examples of applications to k-regular graphs and
Young tableaux with repeated entries are given. Asymptotic estimates are a
natural application of our method, which we illustrate on the same model of
Young tableaux. We also derive a seemingly new formula for the Kronecker
product of the sum of Schur functions with itself.Comment: 51 pages, full paper version of FPSAC 02 extended abstract; v2:
corrections from original submission, improved clarity; now formatted for
journal + bibliograph
Rectangular Matrix Models and Combinatorics of Colored Graphs
We present applications of rectangular matrix models to various combinatorial
problems, among which the enumeration of face-bicolored graphs with prescribed
vertex degrees, and vertex-tricolored triangulations. We also mention possible
applications to Interaction-Round-a-Face and hard-particle statistical models
defined on random lattices.Comment: 42 pages, 11 figures, tex, harvmac, eps
Three and Four Point Functions of Stress Energy Tensors in D=3 for the Analysis of Cosmological Non-Gaussianities
We compute the correlation functions of 3 and 4 stress energy tensors
in D=3 in free field theories of scalars, abelian gauge fields, and fermions,
which are relevant in the analysis of cosmological non-gaussianities. These
correlators appear in the holographic expressions of the scalar and tensor
perturbations derived for holographic cosmological models. The result is simply
adapted to describe the leading contributions in the gauge coupling to the same
correlators also for a non abelian SU(N) gauge theory. In the case of the
bispectrum, our results are mapped and shown to be in full agreement with the
corresponding expressions given in a recent holographic study by Bzowski,
McFadden and Skenderis. In the 4-T case we present the completely traced
amplitude plus all the contact terms. These are expected to appear in a fourth
order extension of the holographic formulas for the 4-point functions of scalar
metric perturbations.Comment: 29 pages, 3 figure
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