相关论文: On Hofstadter's G-sequence

The reduced norm-one group G of a central simple algebra is an inner form of the special linear group, and an involution on the algebra induces an automorphism of G. We study the action of such automorphisms in the cohomology of arithmetic…

In this paper, we consider a generalization of Horadam sequence {w_n} which is defined by the recurrence w_n = aw_n-1 + cw_n-2; if n is even, w_n = bw_n-1 + cw_n-2; if n is odd with arbitrary initial conditions w_0, w_1 and nonzero real…

In [12] was introduced, for cyclic groups, the class of partially filled arrays of the non-zero sum Heffter array that are, as the Heffter arrays, related to difference families, graph decompositions, and biembeddings. Here we generalize…

The golden ratio and Fibonacci numbers are found to occur in various aspects of nature. We discuss the occurrence of this ratio in an interesting physical problem concerning center of masses in two dimensions. The result is shown to be…

This paper is a sequel to our previous paper arXiv:1105.1554, where we defined two types of intermediate Diophantine exponents, connected them to Schmidt exponents and split Dyson's transference inequality into a chain of inequalities for…

Feigin-Semikhatov conjecture, now established, states algebraic isomorphisms between the cosets of the subregular $\mathcal{W}$-algebras and the principal $\mathcal{W}$-superalgebras of type A by their full Heisenberg subalgebras. It can be…

In this paper we present a family of identities for recursive sequences arising from a second order recurrence relation, that gives instances of Zeckendorf representation. We prove these results using a special case of an universal property…

The classical congruences satisfied by the Fibonacci and Lucas sequences are reflected with the decomposition of primes in the ring generated by the gold number. This generalizes to establish a correspondence that we hope will be new…

We revisit Haagerup's enigmatic reduction theorem \cite[Theorems 2.1 \& 3.1]{HJX} showing how that theorem may be extended to general von Neumann algebras $\M$ equipped with an arbitrary faithful normal semifinite weight in a manner which…

We investigate the limiting behavior of multiple ergodic averages along sparse sequences evaluated at prime numbers. Our sequences arise from smooth and well-behaved functions that have polynomial growth. Central to this topic is a…

Inspired by Aldous' conjecture for the spectral gap of the interchange process and its recent resolution by Caputo, Liggett and Richthammer, we define an associated order on the irreducible representations of S_n. Aldous' conjecture is…

Zeckendorf proved that every positive integer has a unique representation as a sum of non-consecutive Fibonacci numbers. A natural generalization of this theorem is to look at the sequence defined as follows: for $n\ge 2$, let $F_{n,1} =…

We present here a relation of different types of Friedrichs models and their use in the description and comprehension of resonance phenomena. We first discuss the basic Friedrichs model and obtain its resonance in the case that this is…

Let g be a random element of a finite classical group G, and let \lambda_{z-1}(g) denote the partition corresponding to the polynomial z-1 in the rational canonical form of g. As the rank of G tends to infinity, \lambda_{z-1}(g) tends to a…

Overlapping gravitational wave (GW) signals are expected in the third-generation (3G) GW detectors, leading to one of the major challenges in GW data analysis. Inference of overlapping GW sources is complicated - it has been reported that…

We give a new construction of q-Genocchi numbers, Euler numbers of higher order, which are different than the q-Genocchi numbers of Cangul-Ozden-Simsek. By using our q-Genoucchi, Euler nimbers of higher order, we can investigate the…

For any graded bialgebras $A$ and $B$, we define a commutative graded algebra $A_B$ representing the functor of $B$-representations of $A$. When $A$ is a cocommutative graded Hopf algebra and $B$ is a commutative ungraded Hopf algebra, we…

In this paper, we discuss the generalized H\"older's inequality in p-summable sequence spaces. In particular, we shall prove sufficient and necessary conditions for generalized H\"older's inequality in those spaces. One of the keys to prove…

In this paper we study generalized Gorenstein Arf rings; a class of one-dimensional Cohen-Macaulay local Arf rings that is strictly contained in the class of Gorenstein rings. We obtain new characterizations and examples of Arf rings, and…

In this essay we'll prove G\"odel's incompleteness theorems twice. First, we'll prove them the good old-fashioned way. Then we'll repeat the feat in the setting of computation. In the process we'll discover that G\"odel's work, rightly…