365 research outputs found
A census of extended generalized quadrangles of order (q-1,q+1) and (q+1,q-1)
We survey the known extended generalized quadrangles with point-residues of order (q - 1, q + 1) and (q + 1,q - 1) and construct a new infinite family of order (q + I,q - 1) (q odd). (C) 1999 Elsevier Science B.V. All rights reserved
Simple maps, Hurwitz numbers, and Topological Recursion
We introduce the notion of fully simple maps, which are maps with non
self-intersecting disjoint boundaries. In contrast, maps where such a
restriction is not imposed are called ordinary. We study in detail the
combinatorics of fully simple maps with topology of a disk or a cylinder. We
show that the generating series of simple disks is given by the functional
inversion of the generating series of ordinary disks. We also obtain an elegant
formula for cylinders. These relations reproduce the relation between moments
and free cumulants established by Collins et al. math.OA/0606431, and implement
the symplectic transformation on the spectral curve in
the context of topological recursion. We conjecture that the generating series
of fully simple maps are computed by the topological recursion after exchange
of and . We propose an argument to prove this statement conditionally to
a mild version of symplectic invariance for the -hermitian matrix model,
which is believed to be true but has not been proved yet.
Our argument relies on an (unconditional) matrix model interpretation of
fully simple maps, via the formal hermitian matrix model with external field.
We also deduce a universal relation between generating series of fully simple
maps and of ordinary maps, which involves double monotone Hurwitz numbers. In
particular, (ordinary) maps without internal faces -- which are generated by
the Gaussian Unitary Ensemble -- and with boundary perimeters
are strictly monotone double Hurwitz numbers
with ramifications above and above .
Combining with a recent result of Dubrovin et al. math-ph/1612.02333, this
implies an ELSV-like formula for these Hurwitz numbers.Comment: 66 pages, 7 figure
A regional land use survey based on remote sensing and other data: A report on a LANDSAT and computer mapping project, volume 2
The author has identified the following significant results. The project mapped land use/cover classifications from LANDSAT computer compatible tape data and combined those results with other multisource data via computer mapping/compositing techniques to analyze various land use planning/natural resource management problems. Data were analyzed on 1:24,000 scale maps at 1.1 acre resolution. LANDSAT analysis software and linkages with other computer mapping software were developed. Significant results were also achieved in training, communication, and identification of needs for developing the LANDSAT/computer mapping technologies into operational tools for use by decision makers
Mini-Workshop: Amalgams for Graphs and Geometries
[no abstract available
Local limit of labeled trees and expected volume growth in a random quadrangulation
Exploiting a bijective correspondence between planar quadrangulations and
well-labeled trees, we define an ensemble of infinite surfaces as a limit of
uniformly distributed ensembles of quadrangulations of fixed finite volume. The
limit random surface can be described in terms of a birth and death process and
a sequence of multitype Galton--Watson trees. As a consequence, we find that
the expected volume of the ball of radius around a marked point in the
limit random surface is .Comment: Published at http://dx.doi.org/10.1214/009117905000000774 in the
Annals of Probability (http://www.imstat.org/aop/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Algebraic methods in random matrices and enumerative geometry
We review the method of symplectic invariants recently introduced to solve
matrix models loop equations, and further extended beyond the context of matrix
models. For any given spectral curve, one defined a sequence of differential
forms, and a sequence of complex numbers Fg . We recall the definition of the
invariants Fg, and we explain their main properties, in particular symplectic
invariance, integrability, modularity,... Then, we give several example of
applications, in particular matrix models, enumeration of discrete surfaces
(maps), algebraic geometry and topological strings, non-intersecting brownian
motions,...Comment: review article, Latex, 139 pages, many figure
A view from infinity of the uniform infinite planar quadrangulation
We introduce a new construction of the Uniform Infinite Planar
Quadrangulation (UIPQ). Our approach is based on an extension of the
Cori-Vauquelin-Schaeffer mapping in the context of infinite trees, in the
spirit of previous work. However, we release the positivity constraint on the
labels of trees which was imposed in these references, so that our construction
is technically much simpler. This approach allows us to prove the conjectures
of Krikun pertaining to the "geometry at infinity" of the UIPQ, and to derive
new results about the UIPQ, among which a fine study of infinite geodesics.Comment: 39 pages, 11 figure
NRRI Collection of Miscellaneous Reports Pt. 2
This is a collection of 24 miscellaneous reports produced by Natural Resources Research Institute, University of Minnesota Duluth; the dates on the reports vary from approximately 1987 to approximately 2000.Natural Resources Research Institute, University of Minnesota Dulut
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