Uniquely-Wilf classes

Two permutations in a class are Wilf-equivalent if, for every size, $n$, the number of permutations in the class of size $n$ containing each of them is the same. Those infinite classes that have only one equivalence class in each size for this relation are characterised provided either that they avoid at least one permutation of size 3, or at least three permutations of size 4.Comment: Updated to DMTCS styl

Higher Spin Chern-Simons Theory and the Super Boussinesq hierarchy

In this paper we construct a map between a solution of supersymmetric Chern-Simons higher spin gravity based on the superalgebra $sl(3|2)$ with Lifshitz scaling and the $N=2$ super Boussinesq hierarchy. We show that under this map the time evolution equations of both theories coincide. In addition, we identify the Poisson structure of the Chern-Simons theory induced by gauge transformation with the second Hamiltonian structure of the super Boussinesq hierarchy.Comment: 22 pages, no figure

Cooperative Data Exchange based on MDS Codes

The cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the $K$ packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that {\it each} of the $K-d$ transmissions is a linear combination of {\it exactly} $d+1$ packets, and we show how to optimally choose the value of $d.$ We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes. Moreover, we show that our method can be used to solve cooperative data exchange problems with weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur

Finite-size corrections to quantized particle transport in topological charge pumps

We investigate the quantization of adiabatic charge transport in the insulating ground state of finite systems. Topological charge pumps are used in experiments as an indicator of topological order. In the thermodynamic limit the transport can be related to a topological Berry phase and is thus strictly quantized. This is no longer true for finite systems. We derive finite-size corrections to the transport both for non-interacting and interacting systems and relate them to analytic properties of the single- and many-body Berry curvature. We find that they depend on the details of experimental realizations of the pumps. While they can be non-negligible even in large systems, a proper choice of the pumping protocol can suppress these corrections

Far-infrared spectroelectrochemistry: a study of linear molybdenum/iron/sulfur clusters

The far-infrared spectroelectrochemistry of linear M/Fe/S (M=Mo, W) complexes was investigated in methylene chloride and dichloroethane. With CsI as spectral windows, bands above 200 cm−1 can be observed in methylene chloride, except for a weak methylene chloride band at 450 cm−1. Substitution of dichloroethane for methylene chloride, solvents of nearly identical electrochemical properties, allows one to observe solute bands in the 450-cm−1 region. The far-infrared spectroelectrochemistry of [MoFe2S4Cl4]2− and its tungsten analogue was investigated. The disappearance of the oxidation bands and the appearance of bands due to the reduced product could be clearly observed. The origin of the vibrational bands could be clearly identified using 34S-substituted complexes. In addition to the far-infrared bands, the resonance Raman spectroelectrochemistry of the oxidized and reduced complex, along with the 34S-substituted complexes was obtained. Far-infrared and resonance Raman spectroelectrochemistry can be combined to understand the electrochemical mechanism of transition metal complexes. The far-infrared spectroelectrochemistry of [MoFe2S4Cl4]2− and its tungsten analogue was investigated. The disappearance of the initial bands and the appearance of bands due to the reduced product could be clearly observed. Resonance Raman spectroscopy and the use of 34S-substituted complexes were used for characterization of the reactant and products