Related papers: Some integer sequences based on derangements
The classical derangement numbers count fixed point-free permutations. In this paper we study the enumeration problem of generalized derangements, when some of the elements are restricted to be in distinct cycles in the cycle decomposition.…
This paper describes a simple method for estimating lower bounds on the number of classes of equivalence for a special kind of integer sequences, called division sequences. The method is based on adding group structure to classes of…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
We introduce the notion of Differential Sequences of ordinary differential equations. This is motivated by related studies based on evolution partial differential equations. We discuss the Riccati Sequence in terms of symmetry analysis,…
Based on tiles and on the Coven-Meyerowitz property, we present some examples and some general constructions of spectral subsets of integers.
We consider the avoidance of patterns in inversion sequences that relate sorting via sorting machines including data structures such as pop stacks and stacks. Such machines have been studied under a variety of additional constraints and…
We define and study a numerical-range analogue of the notion of spectral set. Among the results obtained are a positivity criterion and a dilation theorem, analogous to those already known for spectral sets. An important difference from the…
This note is a survey and collection of results, as well as presenting some original research. For Bessel sequences and frames, the analysis, synthesis and frame operators as well as the Gram matrix are well-known, bounded operators. We…
We generalize an operation described by Sloane on the binary representation of an integer to other bases, thus finding several new sequences.
We formulate a mean-field-like theory of long-range correlated $L$-alphabets sequences, which are actually systems with $(L-1)$ independent parameters. Depending on the values of these parameters, the variance on the average number of any…
A solution is proposed for the problem of composition of ordinary generating functions. A new class of functions that provides a composition of ordinary generating functions is introduced; main theorems are presented; compositae are written…
We provide a setting-independent definition of reals by introducing the notion of a streak. We show that various standard constructions of reals satisfy our definition. We study the structure of reals by noting that its pieces correspond to…
In the setting of nonstandard analysis we introduce the notion of flexible sequence. The terms of flexible sequences are external numbers. These are a sort of analogue for the classical \emph{O$ (\cdot ) $} and \emph{o$ (\cdot ) $} notation…
Sequence alignments are used to capture patterns composed of elements representing multiple conceptual levels through the alignment of sequences that contain overlapping and variable length annotations. The alignments also determine the…
An integer sequence that is defined by initial values and a linear recurrence with constant integer coefficients, can be represented by the difference of two arithmetic terms containing exponentiation. All constants occuring in the term are…
We consider arithmetic sequences, here defined as ordered lists of positive integers. Any such a sequence can be cast onto a quantum state, enabling the quantification of its `surprise' through von Neumann entropy. We identify typical…
Statistical models of word-sense disambiguation are often based on a small number of contextual features or on a model that is assumed to characterize the interactions among a set of features. Model selection is presented as an alternative…
The dominant approach to sequence generation is to produce a sequence in some predefined order, e.g. left to right. In contrast, we propose a more general model that can generate the output sequence by inserting tokens in any arbitrary…
Various spectral notions have been employed to grasp the structure of point sets, in particular non-periodic ones. In this article, we present them in a unified setting and explain the relations between them. For the sake of readability, we…
A mixed graph can be seen as a type of digraph containing some edges (two opposite arcs). Here we introduce the concept of sequence mixed graphs, which is a generalization of both sequence graphs and iterated line digraphs. These structures…