相关论文: Structure of Binary Sequences
Dividing asks about inconsistency along indiscernible sequences. In order to study the finer structure of simple theories without much dividing, the authors recently introduced shearing, which essentially asks about inconsistency along…
We study linear difference equations with variable coefficients in a ring using a new nonlinear method. In a ring with identity, if the homogeneous part of the linear equation has a solution in the unit group of the ring (i.e., a unitary…
Let $\alpha$ and $\beta$ be two nonnegative integers such that $\beta < \alpha$. For an arbitrary sequence $\{a_n\}_{n\geqslant 1}$ of complex numbers, we consider the generalized Lambert series in order to investigate linear combinations…
We introduce several statistics on ordered partitions of sets, that is, set partitions where the blocks are permuted arbitrarily. The distribution of these statistics is closely related to the q-Stirling numbers of the second kind. Some of…
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
We provide the solution to the normal ordering problem for powers and exponentials of two classes of operators. The first one consists of boson strings and more generally homogeneous polynomials, while the second one treats operators linear…
We define a class of algebras describing links of binary semi-isolating formulas on a set of realizations for a family of 1-types of a complete theory. These algebras include algebras of isolating formulas considered before. We prove that a…
We discuss a notion of convergence for binary trees that is based on subtree sizes. In analogy to recent developments in the theory of graphs, posets and permutations we investigate some general aspects of the topology, such as a…
Given an increasing sequence of integers a(n), it is known (due to Weyl) that for almost all reals t, the fractional parts of the dilated sequence t*a(n) are uniformly distributed in the unit interval. Some effort has been made recently to…
Biological sequences do not come at random. Instead, they appear with particular frequencies that reflect properties of the associated system or phenomenon. Knowing how biological sequences are distributed in sequence space is thus a…
We study sequences of partitions of the unit interval into subintervals, starting from the trivial partition, in which each partition is obtained from the one before by splitting its subintervals in two, according to a given rule, and then…
We apply a general approach for distributions of binary isolating and semi-isolating formulas to the class of strongly minimal theories.
We report a rigorous theory to show the origin of the unexpected periodic behavior seen in the consecutive differences between prime numbers. We also check numerically our findings to ensure that they hold for finite sequences of primes,…
Generalized Zeckendorf decompositions are expansions of integers as sums of elements of solutions to recurrence relations. The simplest cases are base-$b$ expansions, and the standard Zeckendorf decomposition uses the Fibonacci sequence.…
Let $q$ be a positive integer and $\mathcal{S}=\left\{x_0,x_1,\ldots,x_{T-1}\right\}\subseteq\mathbb{Z}_q=\{0,1,\ldots,q-1\}$ with $$0\leq x_0<x_1<\ldots< x_{T-1}\leq q-1.$$ We derive from $\mathcal{S}$ three (finite) sequences. 1. For an…
Linear binary fragmentation of synthetic fractal-like agglomerates composed of spherical, equal-size, touching monomers is numerically investigated. Agglomerates of different morphologies are fragmented via random bond removal. The…
For any given sequence of integers there exists a quantum field theory whose Feynman rules produce that sequence. An example is illustrated for the Stirling numbers. The method employed here offers a new direction in combinatorics and graph…
Let us call a sequence of numbers heapable if they can be sequentially inserted to form a binary tree with the heap property, where each insertion subsequent to the first occurs at a leaf of the tree, i.e. below a previously placed number.…
The Stirling number of the second kind $n\brace k$ counts the number of ways to partition a set of $n$ labeled balls into $k$ non-empty unlabeled cells. As an extension of this, we consider $b_1+b_2+\ldots+b_n$ balls with $b_1$ balls…
{\bf Abstract.} Considered is the distribution of the cross correlation between $m$-sequences of length $2^m-1$, where $m$ is even, and $m$-sequences of shorter length $2^{m/2}-1$. The infinite family of pairs of $m$-sequences with…