6,735 research outputs found
Irreducible representations of the symmetric groups from slash homologies of p-complexes
In the 40s, Mayer introduced a construction of (simplicial) -complex by
using the unsigned boundary map and taking coefficients of chains modulo .
We look at such a -complex associated to an -simplex; in which case,
this is also a -complex of representations of the symmetric group of rank
- specifically, of permutation modules associated to two-row compositions.
In this article, we calculate the so-called slash homology - a homology theory
introduced by Khovanov and Qi - of such a -complex. We show that every
non-trivial slash homology group appears as an irreducible representation
associated to two-row partitions, and how this calculation leads to a basis of
these irreducible representations given by the so-called -standard tableaux.Comment: 16 pages, 2 figures. Rewritten the proof of first theorem.
Substantial rearrangement of materials in other sections. Comments welcome
Trumping and Power Majorization
Majorization is a basic concept in matrix theory that has found applications
in numerous settings over the past century. Power majorization is a more
specialized notion that has been studied in the theory of inequalities. On the
other hand, the trumping relation has recently been considered in quantum
information, specifically in entanglement theory. We explore the connections
between trumping and power majorization. We prove an analogue of Rado's theorem
for power majorization and consider a number of examples.Comment: 8 page
Modal logics for reasoning about object-based component composition
Component-oriented development of software supports the adaptability and maintainability of large systems, in particular if requirements change over time and parts of a system have to be modified or replaced. The software architecture in such systems can be described by components
and their composition. In order to describe larger architectures, the composition concept becomes crucial. We will present a formal framework for component composition for object-based software development. The deployment of modal logics for defining components and component composition will allow us to reason about and prove properties of components and compositions
How to Turn an Industry Green: Taxes versus Subsidies
Environmental policies frequently target the ratio of dirty to green output within the same industry. To achieve such targets the green sector may be subsidised or the dirty sector be taxed. This paper shows that in a monopolistic competition setting the two policy instruments have different welfare effects. For a strong green policy (a severe reduction of the dirty sector) a tax is the dominant instrument. For moderate policy targets, a subsidy will be superior (inferior) if the initial situation features a large (small) share of dirty output. These findings have implications for policies such as the Californian Zero Emission Bill or the EU Action Plan for Renewable Energy Sources.Environmental policy; Monopolistic competition; Taxes; Subsidies; Welfare; Zero Emission Bill
XQuery Streaming by Forest Transducers
Streaming of XML transformations is a challenging task and only very few
systems support streaming. Research approaches generally define custom
fragments of XQuery and XPath that are amenable to streaming, and then design
custom algorithms for each fragment. These languages have several shortcomings.
Here we take a more principles approach to the problem of streaming
XQuery-based transformations. We start with an elegant transducer model for
which many static analysis problems are well-understood: the Macro Forest
Transducer (MFT). We show that a large fragment of XQuery can be translated
into MFTs --- indeed, a fragment of XQuery, that can express important features
that are missing from other XQuery stream engines, such as GCX: our fragment of
XQuery supports XPath predicates and let-statements. We then rely on a
streaming execution engine for MFTs, one which uses a well-founded set of
optimizations from functional programming, such as strictness analysis and
deforestation. Our prototype achieves time and memory efficiency comparable to
the fastest known engine for XQuery streaming, GCX. This is surprising because
our engine relies on the OCaml built in garbage collector and does not use any
specialized buffer management, while GCX's efficiency is due to clever and
explicit buffer management.Comment: Full version of the paper in the Proceedings of the 30th IEEE
International Conference on Data Engineering (ICDE 2014
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