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Let $n,k\in\mathbb{N}$ and let $p_{n}$ denote the $n$th prime number. We define $p_{n}^{(k)}$ recursively as $p_{n}^{(1)}:=p_{n}$ and $p_{n}^{(k)}=p_{p_{n}^{(k-1)}}$, that is, $p_{n}^{(k)}$ is the $p_{n}^{(k-1)}$th prime. In this note we…
The Bulgarian Solitaire rule induces a finite dynamical system on the set of integer partitions of $n$. Brandt characterized and counted all cycles in its recurrent set for any given $n$, with orbits parametrized by necklaces of black and…
Let $n \geq 1$, $p$ a prime, and $T(n)$ any representative of the Bousfield class of the telescope $v_n^{-1}F(n)$ of a finite type $n$ complex. Also, let $E_n$ be the Lubin-Tate spectrum, $K(E_n)$ its algebraic $K$-theory spectrum, and…
It is well-known that orthogonal polynomials on the real line satisfy a three-term recurrence relation and conversely every system of polynomials satisfying a three-term recurrence relation is orthogonal with respect to some positive Borel…
The Fibonacci sequence is a sequence of numbers that has been studied for hundreds of years. In this paper, we introduce the new sequence S_{k,n} with initial conditions S_{k,0} = 2b and S_{k,1} = bk + a, which is generated by the…
An existing single resonance model with S11, P11 and P13 Breit-Wiegner resonances in the s-channel has been re-applied to the old pi N --> K Lambda data. It has been shown that the standard set of resonant parameters fails to reproduce the…
A nondecreasing sequence of positive integers is $(\alpha,\beta)$-Conolly, or Conolly-like for short, if for every positive integer $m$ the number of times that $m$ occurs in the sequence is $\alpha + \beta r_m$, where $r_m$ is $1$ plus the…
Let K be a real algebraic number field and let P be the set of Pisot numbers generating K. We show that the elements of P-P are the algebraic integers of K whose images under the action of all embeddings of K into C, other than the identity…
A combinatorial block design $D$ is called $3$-pyramidal if there exists a subgroup $G$ of $\mbox{Aut}(D)$ fixing $3$ points and acting regularly on the other points. If this happens, we say that the design is $3$-pyramidal under $G$. In…
Assume that $\{a_{n};\,n\geq0\}$ is a sequence of positive numbers and $\sum a_{n}^{\,-1}<\infty$. Let $\alpha_{n}=ka_{n}$, $\beta_{n}=a_{n}+k^{2}a_{n-1}$ where $k\in(0,1)$ is a parameter, and let $\{P_{n}(x)\}$ be an orthonormal polynomial…
The Ap\'ery numbers may be defined by a cubic three-term recurrence relation, that is, a three-term relation where the coefficients are polynomials in the index of degree $3$. In this work, we first provide a systematic review of Ap\'ery…
The $K\pi$ vector form factor, $F_+^{K\pi}$, used to reproduce the Belle spectrum of $\tauKpi$ decays is described by means of a three-times subtracted dispersion relation also incorporating constraints from $K_{l3}$ decays. The slope and…
Linear recurrent sequences are those whose elements are defined as linear combinations of preceding elements, and finding recurrence relations is a fundamental problem in computer algebra. In this paper, we focus on sequences whose elements…
This paper investigates property QR(3) for Veronese embeddings over an algebraically closed field of characteristic $3$. We determine the rank index of $(\mathbb{P}^n , \mathcal{O}_{\mathbb{P}^n} (d))$ for all $n \geq 2$, $d \geq 3$,…
We use the grid consisting of bits of 3^n to motivate the definition of 2-adic numbers. Specifically, we exhibit diagonal stripes in the bits of 3^(2^n), which turn out to be the first in an infinite sequence of such structures. Our…
In this paper, we study pattern matching in the set F_{n,k} of fillings of the k x n rectangle with the integers 1,...,kn such that the elements in any column increase from bottom to top. Let P be a column strict tableau of shape 2^k. We…
We study the superconformal index of S-fold theories by using AdS/CFT correspondence. It has been known that the index in the large $N$ limit is reproduced as the contribution of bulk Kaluza-Klein modes. For finite $N$ D3-branes wrapped…
This work explores the (non)-integrability and chaotic dynamics of classical strings in the background of a D3-brane with a non-commutative parameter, within the framework of the AdS/CFT correspondence. Using the Polyakov action, we derive…
In this paper we enumerate $k$-noncrossing RNA pseudoknot structures with given minimum arc- and stack-length. That is, we study the numbers of RNA pseudoknot structures with arc-length $\ge 3$, stack-length $\ge \sigma$ and in which there…
The present paper is devoted to the study of the combinatorics of 216 maximal $C^3$ circular codes --- a particular type of structure arising in the analysis of genomic sequences. Their circularity property is believed to be intimately…