The SW(3/2, 3/2, 2) superconformal algebra is a W algebra with two free parameters. It consists of 3 superconformal currents of spins 3/2, 3/2 and 2. The algebra is proved to be the symmetry algebra of the coset su(2)⊕su(2)⊕su(2) su(2) . At the central charge c = 10 2 the algebra coincides with the superconformal algebra associated to manifolds of G2 holonomy. The unitary minimal models of the ...

In this paper the Pólya Aeppli distribution of order k as a compound Poisson distribution is defined. The probability mass function and recursion formulas are given. We consider the interpretation of the distribution and a definition of the Pólya Aeppli process of order k.

We present the first exact method based on the topology of a metabolic network to find minimal sets of metabolites (called precursors) sufficient to produce a set of target metabolites. In contrast with previous proposals, our model takes into account self-regenerating metabolites involved in cycles, which may be used to generate target metabolites from potential precursors. We analyse the comp...

We enumerate bijectively the family of involutive Baxter permutations according to various parameters; in particular we obtain an elementary proof that the number of involutive Baxter permutations of size 2n with no fixed points is 3·2 n−1

Important and interesting results which are already known such as those by Pólya and Schoenberg in (1958), Başgöze et al. in (1970), and Ali in (1973), and which are related to convex maps of the unit disc are presented in this note by a more general, unified, and different method. The method considers the product of a nontrivial multiplier with the Norlund means, and shows how the known result...

We study Hoeffding decomposable exchangeable sequences with values in a finite set D = {d1, . . . , dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K ≥ 3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.

We establish the preserving log-convexity property for the generalized Pascal triangles. It is an extension of a result of H. Davenport and G. Pólya “On the product of two power series”, who proved that the binomial convolution of two log-convex sequences is log-convex.

This tutorial covers the Dirichlet distribution, Dirichlet process, Pólya urn (and the associated Chinese restaurant process), hierarchical Dirichlet Process, and the Indian buffet process. Apart from basic properties, we describe and contrast three methods of generating samples: stick-breaking, the Pólya urn, and drawing gamma random variables. For the Dirichlet process we first present an inf...

A reduced word of a permutation $w$ is minimal length expression as product simple transpositions. We examine the computational complexity, formulas and (randomized) algorithms for their enumeration. In particular, we prove that Edelman-Greene statistic, defined by S. Billey-B. Pawlowski, typically exponentially large. This implies result B. it has growing expectation. Our established formal ru...

Enumeration of minimal correction sets (MCSes) of conjunctive normal form formulas is a central and highly intractable problem in infeasibility analysis of constraint systems. Often complete enumeration of MCSes is impossible due to both high computational cost and worst-case exponential number of MCSes. In such cases partial enumeration is sought for, finding applications in various domains, i...