837 research outputs found
Antichain cutsets of strongly connected posets
Rival and Zaguia showed that the antichain cutsets of a finite Boolean
lattice are exactly the level sets. We show that a similar characterization of
antichain cutsets holds for any strongly connected poset of locally finite
height. As a corollary, we get such a characterization for semimodular
lattices, supersolvable lattices, Bruhat orders, locally shellable lattices,
and many more. We also consider a generalization to strongly connected
hypergraphs having finite edges.Comment: 12 pages; v2 contains minor fixes for publicatio
The propagator for the step potential using the path decomposition expansion
We present a direct path integral derivation of the propagator in the
presence of a step potential. The derivation makes use of the Path
Decomposition Expansion (PDX), and also of the definition of the propagator as
a limit of lattice paths.Comment: To appear in DICE 2008 conference proceeding
On a Subposet of the Tamari Lattice
We explore some of the properties of a subposet of the Tamari lattice
introduced by Pallo, which we call the comb poset. We show that three binary
functions that are not well-behaved in the Tamari lattice are remarkably
well-behaved within an interval of the comb poset: rotation distance, meets and
joins, and the common parse words function for a pair of trees. We relate this
poset to a partial order on the symmetric group studied by Edelman.Comment: 21 page
Trade finance in East Asia - potential responses to the shortfall
The crisis of 2008 saw many European banks reduce their provision of trade finance in East Asia. Notwithstanding the actions of the G20 and other bodies to redress this, a substantial shortfall in trade finance facilities in the region remains. This article explores the development of this shortfall, and analyses potential responses to it.
These responses range from some much-needed further revisions to the Basle III rules, to deepening of cross-border cooperation, creating a ring-fenced liquidity pool for trade finance, encouraging co-financing among the various providers of trade finance both private and public, and establishing a regional trade finance database. In addition, the article ponders the likelihood of China’s banks beginning to take a substantial role in providing trade finance to the region. Trade finance offers China’s banks a low risk means of expanding into international business, and offers China a way to provide the sort of important service to its region that regional leaders typically seek to provide.postprin
Trade Finance in East Asia: Potential Responses to the Shortfall
The crisis of 2008 saw many European banks reduce their provision of trade finance in East Asia. Notwithstanding the actions of the Group of Twenty and other bodies to redress this, a substantial shortfall in trade finance facilities in the region remains. This article explores the development of this shortfall and analyses potential responses to it. These responses range from some much needed further revisions to the Basel III rules, to the deepening of cross-border cooperation, creating a ring-fenced liquidity pool for trade finance, encouraging co-financing among the various providers of trade finance both private and public and establishing a regional trade finance database. In addition, the article ponders the likelihood of China’s banks beginning to take a substantial role in providing trade finance to the region. Trade finance offers China’s banks a low risk means of expanding into international business and offers China a way to provide the sort of important service to its region that regional leaders typically seek to provide.postprin
Effective Invariant Theory of Permutation Groups using Representation Theory
Using the theory of representations of the symmetric group, we propose an
algorithm to compute the invariant ring of a permutation group. Our approach
have the goal to reduce the amount of linear algebra computations and exploit a
thinner combinatorial description of the invariant ring.Comment: Draft version, the corrected full version is available at
http://www.springer.com
Enumerating Cyclic Orientations of a Graph
Acyclic and cyclic orientations of an undirected graph have been widely
studied for their importance: an orientation is acyclic if it assigns a
direction to each edge so as to obtain a directed acyclic graph (DAG) with the
same vertex set; it is cyclic otherwise. As far as we know, only the
enumeration of acyclic orientations has been addressed in the literature. In
this paper, we pose the problem of efficiently enumerating all the
\emph{cyclic} orientations of an undirected connected graph with vertices
and edges, observing that it cannot be solved using algorithmic techniques
previously employed for enumerating acyclic orientations.We show that the
problem is of independent interest from both combinatorial and algorithmic
points of view, and that each cyclic orientation can be listed with
delay time. Space usage is with an additional setup cost
of time before the enumeration begins, or with a setup cost of
time
Covering Partial Cubes with Zones
A partial cube is a graph having an isometric embedding in a hypercube.
Partial cubes are characterized by a natural equivalence relation on the edges,
whose classes are called zones. The number of zones determines the minimal
dimension of a hypercube in which the graph can be embedded. We consider the
problem of covering the vertices of a partial cube with the minimum number of
zones. The problem admits several special cases, among which are the problem of
covering the cells of a line arrangement with a minimum number of lines, and
the problem of finding a minimum-size fibre in a bipartite poset. For several
such special cases, we give upper and lower bounds on the minimum size of a
covering by zones. We also consider the computational complexity of those
problems, and establish some hardness results
On the non-existence of an R-labeling
We present a family of Eulerian posets which does not have any R-labeling.
The result uses a structure theorem for R-labelings of the butterfly poset.Comment: 6 pages, 1 figure. To appear in the journal Orde
Rigidity and volume preserving deformation on degenerate simplices
Given a degenerate -simplex in a -dimensional space
(Euclidean, spherical or hyperbolic space, and ), for each , , Radon's theorem induces a partition of the set of -faces into two
subsets. We prove that if the vertices of the simplex vary smoothly in
for , and the volumes of -faces in one subset are constrained only to
decrease while in the other subset only to increase, then any sufficiently
small motion must preserve the volumes of all -faces; and this property
still holds in for if an invariant of
the degenerate simplex has the desired sign. This answers a question posed by
the author, and the proof relies on an invariant we discovered
for any -stress on a cell complex in . We introduce a
characteristic polynomial of the degenerate simplex by defining
, and prove that the roots
of are real for the Euclidean case. Some evidence suggests the same
conjecture for the hyperbolic case.Comment: 27 pages, 2 figures. To appear in Discrete & Computational Geometr
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