Related papers: My Favorite Integer Sequences
We prove that five ways to define entry A086377 in the On-Line Encyclopedia of Integer Sequences do lead to the same integer sequence.
User response prediction, which models the user preference w.r.t. the presented items, plays a key role in online services. With two-decade rapid development, nowadays the cumulated user behavior sequences on mature Internet service…
Probabilistic databases (PDBs) model uncertainty in data in a quantitative way. In the established formal framework, probabilistic (relational) databases are finite probability spaces over relational database instances. This finiteness can…
As suggested by the title, this paper is a survey of recent results and questions on the collection of computably enumerable sets under inclusion. This is not a broad survey but one focused on the author's and a few others' current…
In this note we present House of Graphs (http://hog.grinvin.org) which is a new database of graphs. The key principle is to have a searchable database and offer -- next to complete lists of some graph classes -- also a list of special…
An introduction to the On-Line Encyclopedia of Integer Sequences (or OEIS, https://oeis.org) for graduate students in mathematics
In this paper we introduce the concept of completeness of sets. We study this property on the set of integers. We examine how this property is preserved as we carry out various operations compatible with sets. We also introduce the problem…
Let $\{x_1, x_2, ..., x_n\}$ be a vector of real numbers. An integer relation algorithm is a computational scheme to find the $n$ integers $a_k$, if they exist, such that $a_1 x_1 + a_2 x_2 + ... + a_n x_n= 0$. In the past few years,…
Relational Databases are universally conceived as an advance over their predecessors Network and Hierarchical models. Superior in every querying respect, they turned out to be surprisingly incomplete when modeling transitive dependencies.…
The need to analyze information from streams arises in a variety of applications. One of its fundamental research directions is to mine sequential patterns over data streams. Current studies mine series of items based on the presence of the…
Recent work in semantic parsing for question answering has focused on long and complicated questions, many of which would seem unnatural if asked in a normal conversation between two humans. In an effort to explore a conversational QA…
The first author introduced a sequence of polynomials (\cite{8}, sequence A174531) defined recursively. One of the main results of this study is proof of the integrality of its coefficients.
Extending earlier work of R. Donaghey and P. J. Cameron, we investigate some canonical "eigen-sequences" associated with transformations of integer sequences. Several known sequences appear in a new setting: for instance the sequences (such…
A graph is a structure composed of a set of vertices (i.e.nodes, dots) connected to one another by a set of edges (i.e.links, lines). The concept of a graph has been around since the late 19$^\text{th}$ century, however, only in recent…
The first author recently introduced an integer sequence now numbered A355519 in OEIS. This sequence arose from counting bracket tournaments; its study evokes the analysis of the Catalan triangle (sequence A009766 in OEIS) and the related…
This paper provides an introduction to the Patstat patent database. It offers guided examples of ten popular queries that are relevant for research purposes and that cover the most important data tables. It is targeted at academic…
This collection of sums and integrals has been harvested from the mathematical and physical literature in unstructured ways. Its main use is backtracking the original sources whenever an integral of the reader's application resembles one of…
A Sidon sequence is a sequence of integers a_1 < a_2 < a_3 < ... with the property that the sums a_i+a_j (i\le j) are distinct. This work contains a survey of Sidon sequences and their generalizations, and an extensive annotated and…
This paper studies the complexity of query evaluation for databases whose relations are partially ordered; the problem commonly arises when combining or transforming ordered data from multiple sources. We focus on queries in a useful…
The following general idea looks crazy. What if another integer sequence follows each integer sequence like a shadow? I will demonstrate that this is indeed the case, perhaps not for every integer sequence, but for many of them.