相关论文: Indicator function and complex coding for mixed fr…

We show that general $3n-j (n>2)$ symbols of the first kind and the second kind for the group SU(2) can be reformulated in terms of binomial coefficients. The proof is based on the graphical technique established by Yutsis, et al. and…

The number of ordered factorizations and the number of recursive divisors are two related arithmetic functions that are recursively defined. But it is hard to construct explicit representations of these functions. Taking advantage of their…

This work further develops the properties of fractional differential forms. In particular, finite dimensional subspaces of fractional form spaces are considered. An inner product, Hodge dual, and covariant derivative are defined. Coordinate…

Using factorizable Hopf algebras, we construct modular invariant partition functions of charge conjugation, or Cardy, type as characters of coends in categories that share essential features with the ones appearing in logarithmic CFT. The…

This paper demonstrates how to explicitly construct a bidiagonal factorization of the banded recurrence matrix that appears in mixed multiple orthogonality on the step-line in terms of the coeffcients of the mixed multiple orthogonal…

It is shown that if a function defined on the segment [-1,1] has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function's Fourier coefficients $c_n$ for some subset of $n\in[n_1,n_2]$,…

Codes with various kinds of decipherability, weaker than the usual unique decipherability, have been studied since multiset decipherability was introduced in mid-1980s. We consider decipherability of directed figure codes, where directed…

In this paper we factorize matrix polynomials into a complete set of spectral factors using a new design algorithm and we provide a complete set of block roots (solvents). The procedure is an extension of the (scalar) Horner method for the…

The notion of 'bifurcating continued fractions' is introduced. Two coupled sequences of non-negative integers are obtained from an ordered pair of positive real numbers in a manner that generalizes the notion of continued fractions. These…

The Macdonald polynomials expanded in terms of a modified Schur function basis have coefficients called the $q,t$-Kostka polynomials. We define operators to build standard tableaux and show that they are equivalent to creation operators…

The study of combinatorial properties of mathematical objects is a very important research field and continued fractions have been deeply studied in this sense. However, multidimensional continued fractions, which are a generalization…

We will use analytic function theory and Fourier analysis to establish a characterization for some classical umbral calculus, which will focus on the generalization of the evaluation function. Although we cannot cover all the umbral…

To any rooted tree, we associate a sequence of numbers that we call the logarithmic factorials of the tree. This provides a generalization of Bhargava's factorials to a natural combinatorial setting suitable for studying questions around…

We continue to investigate which polynomials can possibly occur as factors in the denominators of rational solutions of a given partial linear difference equation. In an earlier article we had introduced the distinction between periodic and…

Orthogonal arrays are arguably one of the most fascinating and important statistical tools for efficient data collection. They have a simple, natural definition, desirable properties when used as fractional factorials, and a rich and…

We investigate a collection of orthonormal functions that encodes information about the continued fraction expansion of real numbers. When suitably ordered these functions form a complete system of martingale differences and are a special…

We define a q-chromatic function on graphs, list some of its properties and provide some formulas in the class of general chordal graphs. Then we relate the q-chromatic function to the colored Jones function of knots. This leads to a…

Considering the large number of fractional operators that exist, and since it does not seem that their number will stop increasing soon at the time of writing this paper, it is presented for the first time, as far as the authors know, a…

The connection between continued fractions and orthogonality which is familiar for $J$-fractions and $T$-fractions is extended to what we call $R$-fractions of type I and II. These continued fractions are associated with recurrence…

The signs of Fourier coefficients of certain eta quotients are determined by dissecting expansions for theta functions and by applying a general dissection formula for certain classes of quintuple products. A characterization is given for…