Computing the Ball Size of Frequency Permutations under Chebyshev Distance

Let $S_n^\lambda$ be the set of all permutations over the multiset $\{\overbrace{1,...,1}^{\lambda},...,\overbrace{m,...,m}^\lambda\}$ where $n=m\lambda$. A frequency permutation array (FPA) of minimum distance $d$ is a subset of $S_n^\lambda$ in which every two elements have distance at least $d$. FPAs have many applications related to error correcting codes. In coding theory, the Gilbert-Varshamov bound and the sphere-packing bound are derived from the size of balls of certain radii. We propose two efficient algorithms that compute the ball size of frequency permutations under Chebyshev distance. Both methods extend previous known results. The first one runs in $O({2d\lambda \choose d\lambda}^{2.376}\log n)$ time and $O({2d\lambda \choose d\lambda}^{2})$ space. The second one runs in $O({2d\lambda \choose d\lambda}{d\lambda+\lambda\choose \lambda}\frac{n}{\lambda})$ time and $O({2d\lambda \choose d\lambda})$ space. For small constants $\lambda$ and $d$, both are efficient in time and use constant storage space.Comment: Submitted to ISIT 201

On the Emergence and Evolution of Mark-up Middlemen: An Inframarginal Model

This paper is aimed to provide an economic interpretation on the emergence and evolution of the specialised middlemen whose duty is to facilitate the transactions of goods and services in an economy. In a general equilibrium framework, the emergence and evolution of the specialised middlemen conforms to Adam Smith’s insight of deepening specialisation and the division of labour with the improvement in institutions and/or transaction technologies. Consequently, the emergence and the growth of the intermediation sector in both absolute and relative terms, the expansion of the network which provides transaction services, the evolution of market structure from autarky towards division of labour, the improvement in productivity, the reduction in wholesaling-retailing price dispersion, will be realised in concurrencymiddlemen, transaction efficiency, inframarginal economics

\Lambda_b Lifetime from the HQET Sum Rule

The HQET sum rule analysis for the \Lambda_b matrix element of the four-quark operator relevant to its lifetime is reported. Our main conclusion is that the lifetime ratio \tau(\Lambda_b)/\tau(B^0) can be as low as 0.91.Comment: 5 pages, latex, no figures, uses sprocl.sty (included). Talk by C. Liu at Int. Conf. on Flavor Phys., Zhang-Jia-Jie, 31/5-6/6 200