A combinatorial bijection is given between pairs of permutations in S, the product of which is a given n-cycle and two-coioured plane edge-rooted trees on n edges, when the numbers of cycles in the disjoint cycle representations of the permutations sum to n + 1. Thus the corresponding connection coefficient for the symmetric group is determined by enumerating these trees with respect to appropr...

A power series is introduced that is an extension to three sets of variables of the Cauchy sum for Jack symmetric functions in the Jack parameter α. We conjecture that the coefficients of this series with respect to the power sum basis are nonnegative integer polynomials in b, the Jack parameter shifted by 1. More strongly, we make the Matchings-Jack Conjecture, that the coefficients are counti...

Associations between childhood disorders and parenting were investigated on a sample comprising of 290 boys and girls in the ages (7–13 yrs), collected from Patiala city. Significant t tests indicated high anxiety and affective problems in girls while boys were found to be higher on conduct problems. Parental connection and regulation were found to be negatively associated with childhood disord...

An arrangement is a finite set of hyperplanes in a finite dimensional complex affine space. A complex rank one local system on the arrangement complement is determined by a set of complex weights for the hyperplanes. We study the Gauss-Manin connection for the moduli space of arrangements of fixed combinatorial type in the cohomology of the complement with coefficients in the local system deter...

In this paper, based on the author’s lectures at the 1995 les Houches Summer school, explicit expressions for the Friedan–Shenker connection on the vector bundle of WZW conformal blocks on the moduli space of curves with tangent vectors at n marked points are given. The covariant derivatives are expressed in terms of “dynamical r-matrices”, a notion borrowed from integrable systems. The case of...

In this paper, an integrated approach is proposed for non-recursive formulation of connection coefficients of different orthogonal functions in terms of a generic orthogonal function. The application of these coefficients arises when the product of two orthogonal basis functions are to be expressed in terms of single basis functions. Two significant advantages are achieved; one, the non-recursi...

has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equiva...

Abstract. Several new transformations for q-binomial coefficients are found, which have the special feature that the kernel is a polynomial with nonnegative coefficients. By studying the group-like properties of these positivity preserving transformations, as well as their connection with the Bailey lemma, many new summation and transformation formulas for basic hypergeometric series are found....

We establish a connection between the orbifold cohomology of hypertoric varieties and the Ehrhart theory of Lawrence polytopes. More specifically, we show that the dimensions of the orbifold cohomology groups of a hypertoric variety are equal to the coefficients of the Ehrhart δ-polynomial of the associated Lawrence polytope. As a consequence, we deduce a formula for the Ehrhart δ-polynomial of...

We investigate invariant random fields on the sphere using a new type of spherical wavelets, called needlets. These are compactly supported in frequency and enjoy excellent localization properties in real space, with quasi-exponentially decaying tails. We show that, for random fields on the sphere, the needlet coefficients are asymptotically uncorrelated for any fixed angular distance. This pro...