The aim of this study is to manipulate musical cues systematically to determine the aspects of music that contribute to emotional expression, and whether these cues operate in additive or interactive fashion, and whether the cue levels can be characterized as linear or non-linear. An optimized factorial design was used with six primary musical cues (mode, tempo, dynamics, articulation, timbre, ...

We give a combinatorial interpretation for the super Catalan number S(m,m + s) for s ≤ 3 using lattice paths and make an attempt at a combinatorial interpretation for s = 4. We also examine the integrality of some factorial ratios.

Recently, Kim-Kim [10] have studied type 2-Changhee and Daehee polynomials. They also introduced the 2-Bernoulli polynomials in order to express central factorial numbers of second kind by making use negative integral orders. Inspired their work, we consider a new class generating functions We give some identities for these including 2-Euler Stirling kind.

For each infinite series of the classical Lie groups of type B, C or D, we introduce a family of polynomials parametrized by the elements of the corresponding Weyl group of infinite rank. These polynomials represent the Schubert classes in the equivariant cohomology of the appropriate flag variety. They satisfy a stability property, and are a natural extension of the (single) Schubert polynomia...

The Strong Factorial Conjecture of E. Edo and A. van den Essen [3] is concerned with the linear functional L on the space of complex polynomials defined by sending a monomial generator z1 1 · · · zn n to (a1!) · · · (an!). The conjecture asserts that for a non-zero multi-variable complex polynomial F , the maximum number of consecutive zeroes that may appear in the sequence {L(F ) : n ≥ 1} is N...

In the context of algebraic statistics an experimental design is described by a set of polynomials called the design ideal. This, in turn, is generated by finite sets of polynomials. Two types of generating sets are mostly used in the literature: Gröbner bases and indicator functions. We briefly describe them both, how they are used in the analysis and planning of a design and how to switch bet...

Integer-valued polynomials on subsets of discrete valuation domains are well studied. We undertake here a systematical study of integer-valued polynomials on subsets S of valued fields and of several connected notions: the polynomial closure of S, the Bhargava’s factorial ideals of S and the v-orderings of S. A sequence of numbers is naturally associated to the subset S and a good description c...

Let S ⊆ Z. The generalized factorial function for S, denoted n!S , is introduced in accordance with theory already established by Bhargava ([4]). Along with several known theorems about these functions, a number of other issues will be explored. This Thesis is divided into 4 chapters. Chapter 1 provides the necessary definitions and offers a connection between the generalized factorial function...

Factorial Schur functions are generalizations of Schur functions that have, in addition to the usual variables, a second family of “shift” parameters. We show that a factorial Schur function times a deformation of the Weyl denominator may be expressed as the partition function of a particular statistical-mechanical system (six-vertex model). The proof is based on the Yang-Baxter equation. There...