116 research outputs found
Low speed wind tunnel investigation of a four-engine upper surface blown model having swept wing and rectangular and D-shaped exhaust nozzles
A low speed investigation was conducted in the Langley V/STOL tunnel to determine the power-on static-turning and powered-lift aerodynamic performance of a four engine upper surface blown transport configuration. Initial tests with a D-shaped exhaust nozzle showed relatively poor flow-turning capability, and the D-nozzles were replaced by rectangular nozzles with a width-height ratio of 6.0. The high lift system consisted of a leading edge slat and two different trailing-edge-flap configurations. A double slotted flap with the gaps sealed was investigated and a simple radius flap was also tested. A maximum lift coefficient of approximately 9.3 was obtained for the model with the rectangular exhaust nozzles with both the double slotted flap deflected 50 deg and the radius flap deflected 90 deg
Wing surface-jet interaction characteristics of an upper-surface blown model with rectangular exhaust nozzles and a radius flap
The wing surface jet interaction characteristics of an upper surface blown transport configuration were investigated in the Langley V/STOL tunnel. Velocity profiles at the inboard engine center line were measured for several chordwise locations, and chordwise pressure distributions on the flap were obtained. The model represented a four engine arrangement having relatively high aspect ratio rectangular spread, exhaust nozzles and a simple trailing edge radius flap
Grothendieck bialgebras, Partition lattices, and symmetric functions in noncommutative variables
We show that the Grothendieck bialgebra of the semi-tower of partition lattice algebras is isomorphic to the graded dual of the bialgebra of symmetric functions in noncommutative variables. In particular this isomorphism singles out a canonical new basis of the symmetric functions in noncommutative variables which would be an analogue of the Schur function basis for this bialgebra
Polyhedral models for generalized associahedra via Coxeter elements
Motivated by the theory of cluster algebras, F. Chapoton, S. Fomin and A.
Zelevinsky associated to each finite type root system a simple convex polytope
called \emph{generalized associahedron}. They provided an explicit realization
of this polytope associated with a bipartite orientation of the corresponding
Dynkin diagram.
In the first part of this paper, using the parametrization of cluster
variables by their -vectors explicitly computed by S.-W. Yang and A.
Zelevinsky, we generalize the original construction to any orientation. In the
second part we show that our construction agrees with the one given by C.
Hohlweg, C. Lange, and H. Thomas in the setup of Cambrian fans developed by N.
Reading and D. Speyer.Comment: 31 pages, 2 figures. Changelog: 20111106: initial version 20120403:
fixed errors in figures 20120827: revised versio
Associahedra via spines
An associahedron is a polytope whose vertices correspond to triangulations of
a convex polygon and whose edges correspond to flips between them. Using
labeled polygons, C. Hohlweg and C. Lange constructed various realizations of
the associahedron with relevant properties related to the symmetric group and
the classical permutahedron. We introduce the spine of a triangulation as its
dual tree together with a labeling and an orientation. This notion extends the
classical understanding of the associahedron via binary trees, introduces a new
perspective on C. Hohlweg and C. Lange's construction closer to J.-L. Loday's
original approach, and sheds light upon the combinatorial and geometric
properties of the resulting realizations of the associahedron. It also leads to
noteworthy proofs which shorten and simplify previous approaches.Comment: 27 pages, 11 figures. Version 5: minor correction
Near-Optimal Computation of Runs over General Alphabet via Non-Crossing LCE Queries
Longest common extension queries (LCE queries) and runs are ubiquitous in
algorithmic stringology. Linear-time algorithms computing runs and
preprocessing for constant-time LCE queries have been known for over a decade.
However, these algorithms assume a linearly-sortable integer alphabet. A recent
breakthrough paper by Bannai et.\ al.\ (SODA 2015) showed a link between the
two notions: all the runs in a string can be computed via a linear number of
LCE queries. The first to consider these problems over a general ordered
alphabet was Kosolobov (\emph{Inf.\ Process.\ Lett.}, 2016), who presented an
-time algorithm for answering LCE queries. This
result was improved by Gawrychowski et.\ al.\ (accepted to CPM 2016) to time. In this work we note a special \emph{non-crossing} property
of LCE queries asked in the runs computation. We show that any such
non-crossing queries can be answered on-line in time, which
yields an -time algorithm for computing runs
Coloured peak algebras and Hopf algebras
For a finite abelian group, we study the properties of general
equivalence relations on G_n=G^n\rtimes \SG_n, the wreath product of with
the symmetric group \SG_n, also known as the -coloured symmetric group. We
show that under certain conditions, some equivalence relations give rise to
subalgebras of \k G_n as well as graded connected Hopf subalgebras of
\bigoplus_{n\ge o} \k G_n. In particular we construct a -coloured peak
subalgebra of the Mantaci-Reutenauer algebra (or -coloured descent algebra).
We show that the direct sum of the -coloured peak algebras is a Hopf
algebra. We also have similar results for a -colouring of the Loday-Ronco
Hopf algebras of planar binary trees. For many of the equivalence relations
under study, we obtain a functor from the category of finite abelian groups to
the category of graded connected Hopf algebras. We end our investigation by
describing a Hopf endomorphism of the -coloured descent Hopf algebra whose
image is the -coloured peak Hopf algebra. We outline a theory of
combinatorial -coloured Hopf algebra for which the -coloured
quasi-symmetric Hopf algebra and the graded dual to the -coloured peak Hopf
algebra are central objects.Comment: 26 pages latex2
Geometric combinatorial algebras: cyclohedron and simplex
In this paper we report on results of our investigation into the algebraic
structure supported by the combinatorial geometry of the cyclohedron. Our new
graded algebra structures lie between two well known Hopf algebras: the
Malvenuto-Reutenauer algebra of permutations and the Loday-Ronco algebra of
binary trees. Connecting algebra maps arise from a new generalization of the
Tonks projection from the permutohedron to the associahedron, which we discover
via the viewpoint of the graph associahedra of Carr and Devadoss. At the same
time that viewpoint allows exciting geometrical insights into the
multiplicative structure of the algebras involved. Extending the Tonks
projection also reveals a new graded algebra structure on the simplices.
Finally this latter is extended to a new graded Hopf algebra (one-sided) with
basis all the faces of the simplices.Comment: 23 figures, new expanded section about Hopf algebra of simplices,
with journal correction
Multi-triangulations as complexes of star polygons
Maximal -crossing-free graphs on a planar point set in convex
position, that is, -triangulations, have received attention in recent
literature, with motivation coming from several interpretations of them.
We introduce a new way of looking at -triangulations, namely as complexes
of star polygons. With this tool we give new, direct, proofs of the fundamental
properties of -triangulations, as well as some new results. This
interpretation also opens-up new avenues of research, that we briefly explore
in the last section.Comment: 40 pages, 24 figures; added references, update Section
- …