相关论文: My Favorite Integer Sequences
In this book we use only special types of intervals and introduce the notion of different types of interval linear algebras and interval vector spaces using the intervals of the form [0, a] where the intervals are from Zn or Z+ \cup {0} or…
An elementary method for computing various prime sequences using the sequence of Farey sequences is described.
The paperfolding sequences form an uncountable class of infinite sequences over the alphabet $\{ -1, 1 \}$ that describe the sequence of folds arising from iterated folding of a piece of paper, followed by unfolding. In this note we observe…
Suppose we have just performed searches in a self-index for two patterns $A$ and $B$ and now we want to search for their concatenation \A B); how can we best make use of our previous computations? In this paper we consider this problem and,…
Network latency distributions, their algebra, and use examples. This paper considers modeling of capacity-insensitive processes and distributed systems. It provides algebraic properties of the latency distribution algebra and Haskell code…
Structured prediction problems are one of the fundamental tools in machine learning. In order to facilitate algorithm development for their numerical solution, we collect in one place a large number of datasets in easy to read formats for a…
This note presents a discussion of the algebraic and combinatorial aspects of the theory of pure O-sequences. Various instances where pure O-sequences appear are described. Several open problems that deserve further investigation are also…
Frequent pattern mining is widely used to find ``important'' or ``interesting'' patterns in data. While it is not easy to mathematically define such patterns, maximal frequent patterns are promising candidates, as frequency is a natural…
Based on Euclid's algorithm, we find a kind of special sequences which play an interesting role in the study of primes. We call them W Sequences. They not only ties up the distribution of primes in short interval but also enables us to give…
Mixture models have been around for over 150 years, as an intuitively simple and practical tool for enriching the collection of probability distributions available for modelling data. In this chapter we describe the basic ideas of the…
This paper is concerned with the problem of expressing three consecutive integers as sums of three cubes. We give several parametric solutions of the problem. We also give somewhat trivial solutions of five or seven consecutive integers…
Repairing inconsistent knowledge bases is a task that has been assessed, with great advances over several decades, from within the knowledge representation and reasoning and the database theory communities. As information becomes more…
Graph databases have become essential tools for managing complex and interconnected data, which is common in areas like social networks, bioinformatics, and recommendation systems. Unlike traditional relational databases, graph databases…
Recent sequential pattern mining methods have used the minimum description length (MDL) principle to define an encoding scheme which describes an algorithm for mining the most compressing patterns in a database. We present a novel…
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
The paper contains a discussion on a number of open problems in queueing theory. Some of them are known for decades, some are more recent. They relate to stability and to rare events. There is an idea to prepare a special issue of QUESTA on…
We consider the problem of enumerating integer tetrahedra of fixed perimeter (sum of side-lengths) and/or diameter (maximum side-length), up to congruence. As we will see, this problem is considerably more difficult than the corresponding…
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.
The Linked Data Paradigm is one of the most promising technologies for publishing, sharing, and connecting data on the Web, and offers a new way for data integration and interoperability. However, the proliferation of distributed,…
We study the integer sequence v_n of numbers of lines in hypersurfaces of degree 2n-3 of P^n, n>1. We prove a number of congruence properties of these numbers of several different types. Furthermore, the asymptotics of the v_n are described…