相关论文: Chung-Graham and Zeckendorf representations
The problem of exponentiating derivations of quasi *-algebras is considered in view of applying it to the determination of the time evolution of a physical system. The particular case where observables constitute a proper CQ*-algebra is…
Some generalized multi-sum Chu-Vandermonde identities are presented and proved, generalizing some known multi-sum Chu-Vandermonde identities from literature and adding some quadratic and cubic examples of these identities. Some other…
We consider relationships between cubic algebras and implication algebras. We first exhibit a functorial construction of a cubic algebra from an implication algebra. Then we consider an collapse of a cubic algebra to an implication algebra…
We revisit a classic theorem of Frougny and Sakarovitch concerning automata for $\varphi$-representations, and show how to obtain it in a different and more computationally direct way. Using it, we can find simple, induction-free proofs of…
We discuss a fine tuning of the co- and contra-variant transforms through construction of specific fiducial and reconstructing vectors. The technique is illustrated on three different forms of induced representations of the Heisenberg…
The representations of a $k$-graph $C^*$-algebra $C^*(\Lambda)$ which arise from $\Lambda$-semibranching function systems are closely linked to the dynamics of the $k$-graph $\Lambda$. In this paper, we undertake a systematic analysis of…
We characterize the generating function of the number of representations described in the title in terms of the theory of modular forms. Appealing to this characterization we obtain explicit formulas for the representation numbers as…
We give formulas for the number of representations of non negative integers by various quadratic forms. We also give evaluations in the case of sum of two cubes (cubic case) and the quintic case, as well. We introduce a class of generalized…
We study q-integral representations of the q-gamma and the q-beta functions. This study leads to a very interesting q-constant. As an application of these integral representations, we obtain a simple conceptual proof of a family of…
We provide two kinds of representations for the Taylor coefficients of the Weierstrass $\sigma$-function $\sigma(\cdot;\Gamma)$ associated to an arbitrary lattice $\Gamma$ in the complex plane $\mathbb{C}=\mathbb{R}^2$ - the first one in…
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for…
Chung and Graham began the systematic study of k-uniform hypergraph quasirandom properties soon after the foundational results of Thomason and Chung-Graham-Wilson on quasirandom graphs. One feature that became apparent in the early work on…
Motivated by the harmonic analysis of self-affine measures, we introduce a class of representations of the Cuntz algebra associated to random walks on graphs. The representations are constructed using the dilation theory of row…
Certain famous combinatorial sequences, such as the Catalan numbers and the Motzkin numbers, when taken modulo a prime power, can be computed by finite automata. Many theorems about such sequences can therefore be proved using Walnut, which…
The aim of this note is to prove a representation theorem for left--invariant functionals in Carnot groups. As a direct consequence, we can also provide a $\Gamma$-convergence result for a smaller class of functionals.
We derive the recurrence relations for relativistic Coulomb integrals directly from the integral representations with the help of computer algebra methods. In order to manage the computational complexity of this problem, we employ holonomic…
We discuss an interesting sequence defined recursively; namely, sequence A105774 from the On-Line Encyclopedia of Integer Sequences, and study some of its properties. Our main tools are Fibonacci representation, finite automata, and the…
In this paper, we discuss a method of constructing separable representations of the $C^*$-algebras associated to strongly connected row-finite $k$-graphs $\Lambda$. We begin by giving an alternative characterization of the…
We provide a complete characterisation of the appearance function for paper-folding sequences for factors of any length. We make use of the software package {\tt Walnut} to establish these results.
The optimal calculation order of a computational graph can be represented by a set of algebraic expressions. Computational graph and algebraic expression both have close relations and significant differences, this paper looks into these…