In type A, the q,tFussCatalan numbers can be defined as a bigraded Hilbert series of a module associated to the symmetric group. We generalize this construction to (finite) complex reflection groups and, based on computer experiments, we exhibit…
Papers in Algebra
Algebra papers in Mathematics, Q
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in Algebra, Q


Identifying a subset of features that preserves classification accuracy is a problem of growing importance, because of the increasing size and dimensionality of realworld data sets. We propose a new feature selection method, named Quadratic…

Quadrature signal processing is used in many fields of science and engineering, and quadrature signals are necessary to describe the processing and implementation that takes place in modern digital communications systems. In this tutorial we'll…

We examine a theory of competitive innovation in which new ideas are introduced only when diminishing returns to the use of existing ideas sets in. After an idea is introduced, the knowledge capital associated with that idea expands, and its value…

Teamwork is a fundamental aspect of many human activities, from business to art and from sports to science. Recent research suggest that team work is of crucial importance to cuttingedge scientific research, but little is known about how teamwork…

We investigate the edge conductance of particles submitted to an Iwatsuka magnetic field, playing the role of a purely magnetic barrier. We also consider magnetic guides generated by generalized Iwatsuka potentials. In both cases we prove…

Quantum cryptography could well be the first application of quantum mechanics at the singlequantum level. The rapid progress in both theory and experiment in recent years is reviewed, with emphasis on open questions and technological issues.

An encryption scheme is said to be entropically secure if an adversary whose minentropy on the message is upper bounded cannot guess any function of the message. Similarly, an encryption scheme is entropically indistinguishable if the encrypted…

It is shown that 2+1 dimensional quantum YangMills theory, with an action consisting purely of the ChernSimons term, is exactly soluble and gives a natural framework for understanding the Jones polynomial of knot theory in three dimensional terms.…

We prove that the selfinteracting scalar field on the fourdimensional degenerate Moyal plane is renormalisable to all orders when adding a suitable counterterm to the Lagrangean. Despite the apparent simplicity of the model, it raises several non…

The purpose of this Note is to unify quantum groups and starproducts under a general umbrella: quantum groupoids. It is shown that a quantum groupoid naturally gives rise to a Lie bialgebroid as a classical limit. The converse question, i.e., the…

We classify the compact quantum groups acting on 4 points. These are the quantum subgroups of the quantum permutation group $\mathcal Q_4$. Our main tool is a new presentation for the algebra $\rm C(\mathcal Q_4)$, corresponding to an isomorphism of…

We introduce and study two new examples of noncommutative spheres: the halfliberated sphere, and the free sphere. Together with the usual sphere, these two spheres have the property that the corresponding quantum isometry group is "easy", in the…

Lefthanded metamaterials make perfect lenses that image classical electromagnetic fields with significantly higher resolution than the diffraction limit. Here we consider the quantum physics of such devices. We show that the Casimir force of two…

This paper investigates quantum logic from the perspective of categorical logic, and starts from minimal assumptions, namely the existence of involutions/daggers and kernels. The resulting structures turn out to (1) encompass many examples of…

On the basis of introspective analysis, we establish a crucial requirement for the physical computation basis of consciousness: it should allow processing a significant amount of information together at the same time. Classical computation does not…

In this paper a programming language, qGCL,is presented for the expression of quantum algorithms. It contains the features re quired to program a ‘universal’ quantum computer (including initiali sation and observation), has a formal semantics and…

We study the discretetime quantum walkbased search for a marked vertex on a graph. By considering various structures in which not all vertices are equivalent, we investigate the relationship between the successful search probability and the…

We introduce a large equivalence class of graph properties, all of which are shared by socalled random graphs. Unlike random graphs, however, it is often relatively easy to verify that a particular family of graphs possesses some property in this…

We present a practical and efficient means to compute the singular value decomposition (SVD) of a real or complex quaternion matrix A based on bidiagonalization of A to a real or complex bidiagonal matrix B using quaternionic Householder…
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