User:Charles R Greathouse IV/Projects

There are a number of mathematical projects, sites, or programs ("projects" for short) which are similar to (at least one aspect of) the OEIS. This page is an attempt to describe and list some of these projects.

Properties

Billey & Tenner's Fingerprint databases for theorems is a key resource. They suggest that the purpose of projects is to encode theorems with a fingerprint satisfying these conditions:

• Should be language independent.
• Should reference existing literature.
• Should be collaborative and publicly available.
• Should be encoded in a small amount of data.

List of projects: integer sequences

On-Line Encyclopedia of Integer Sequences

This is Billey & Tenner's prime example of a fingerprint database for theorems, listed here only for completeness.

Sequencer

A project by Philipp Emanuel Weidmann.

• sequencer on github, last updated Mar 7, 2015
• SequenceBoss - broken link, once an online implementation of Sequencer

Integer Sequences

Tony D. Noe's collection of about a thousand integer sequences, started in 2014. Includes formulas, graphs, Mathematica programs, and references (but unfortunately no search features). Text is apparently freeform; metadata consists of OEIS-inspired keywords: base, cons, fini, full, hard, more, nice, nonn, sign, tabf, tabl. Entries are crosslinked with other entries and also with OEIS entries.

• Integer Sequences
• backup link

Sequence Machine

An automated sequence database by Jon Maiga. It describes itself as "A database with 1659045 machine generated integer and decimal sequences." (as of 2022) Contains sequence tags (like expanded keywords), function tags, OEIS references, and attempts at combining identical sequences with different definitions.

• Sequence Machine

List of projects: combinatorics

Database of Permutation Pattern Avoidance

A database of permutations which avoid a finite number of permutation patterns. Permutations can be searched by a subset of the avoided patterns and/or by keyword. Contains 54 entries as of Oct 2018. Data for each entry includes the avoided pattern(s), a title, references, the enumeration (a name, formula, or generating function), an OEIS reference for the enumeration, and the contributor.

• Database of Permutation Pattern Avoidance

The Combinatorial Statistic Finder

Finds combinatorial statistics. Different types of search are available based on the type of statistic searched for (out of these 17):

• Alternating sign matrices; binary trees; cores; Dyck paths; finite Cartan types; Gelfand-Tsetlin patterns; graphs; integer compositions; integer partitions; ordered trees; parking functions; perfect matchings; permutations; posets; semistandard tableaux; set partitions; standard tableaux

As of Oct 2018 there were 1278 statistics in the database. Data for each statistic includes values, description, code, references, and author.

• The Combinatorial Statistic Finder
• Chris Berg, Viviane Pons, Travis Scrimshaw, Jessica Striker, Christian Stump, FindStat - the combinatorial statistics database, 2014, 2 pp. arXiv:1401.3690 (math.CO; cs.DB)

Hypergeometric series / WZ method / A = B

A method for finding hypergeometric identities or proving their nonexistence. Software support exists in Maple and Mathematica.

• A = B
• Related programs

gfun

Algorithmic detection of generating functions from Maple. Written by Bruno Salvy and Paul Zimmermann.

• The gfun package
• Overview of the gfun Package
• GFUN: a Maple package for the manipulation of generating and holonomic functions in one variable (1994)
• Marc Mezzarobba, Numgfun: a package for numerical and analytic computation with D-finite functions, Proceedings of the 2010 international symposium on symbolic and algebraic computation (issac 2010), ACM, pages 139-145, 2010. arXiv:1002.3077 (cs.SC)

The Combinatorial Object Server++

• The Combinatorial Object Server++

List of projects: constants

RIES

Robert Munafo's tool to "find algebraic equations, given their solution". Uses a bidirectional search to find candidates of length n in time Õ(2^n/2). Available online or for download (C source).

• RIES
• Randall Munroe, Approximations

Inverse Symbolic Calculator

Simon Plouffe's tool for detecting real numbers appearing in various forms. Apparently a private form also exists, which can be queried by request to Simon Plouffe via email.

• isc+

Numbers Aplenty

Giovanni Resta's collection of properties of integer sequences and integers (up to 10¹⁵), mostly with respect to those properties. As of 2024 the page has 194 properties, mostly relating to prime numbers or base 10.

• Numbers Aplenty

Shamos’s Catalog of the Real Numbers

A 700-page list of constants, defining formulas, and references.

• Michael Ian Shamos, Shamos’s Catalog of the Real Numbers (2011). 700 pp.
• Michael Ian Shamos, A Catalog of the Real Numbers (2007), 667 pp.

List of projects: algebra

Groupprops

Vipul Naik's brainchild, a wiki with 7000+ pages collecting information on the properties of various groups, especially finite groups. The project dates back to 2006 (2008 in its present form). Data includes presence or absence of common group properties, membership in various families, morphisms, and conjugacy class structure. GAP code is often included. Text searches are the primary way to find pages, though there is a query creator which allows searching by category as well.

• Groupprops, The Group Properties Wiki
• Subject wikis (a collection of other wikis on other subjects, much smaller than groupprops)

The Number Fields Database

John Jones and David Roberts

An extension of an older project by John Jones at [1].

• The Number Fields Database
• John W. Jones and David P. Roberts, A database of number fields, LMS J. Comput. Math. 17:1 (2014), pp. 595-618. arXiv:1404.0266 (math.NT) alternate link
• Eric Driver, A Number Fields Database, Atelier PARI/GP 2016
• NumberFields@home

A Database for Number Fields

A collection of transitive groups by degree, created by Jürgen Klüners and Gunter Malle in 2001. It contains (as of 2022) all A002106(n) groups for n = 2-23 for a total of 4952 groups; note that the next term, A002106(24) = 25000, is significantly larger than the total. (When released, it contained degrees up to 15.)

• A Database for Number Fields
• Jürgen Klüners and Gunter Malle, A database for field extensions of the rationals, LMS J. Comput. Math. 4 (2001), pp. 182-196. arXiv:math/0102232 (math.NT)

List of projects: number theory

L-functions and modular forms database

The L-functions and modular forms database (LMFDB) collects number-theoretical objects such as L-functions, L-function zeros, elliptic curves, Maass forms, and number fields.

• LMFDB

Database of continued fractions of polynomial type

This rather interesting database lives, for the moment at least, inside the TeX source of this arXiv preprint. As of its initial release, it contains 1307 continued fractions.

• Henri Cohen, A database of continued fractions of polynomial type, arXiv preprint (2024). arXiv:2409.06086 [math.NT]

List of projects: graph theory

House of Graphs

A searchable database of interesting graphs developed by G. Brinkmann, J. Goedgebeur, H. Mélot, K. Coolsaet, and Sven D’hondt.

The database allows searches by text and any of these 33 graph invariants:

• algebraic connectivity, average degree, chromatic index, chromatic number, circumference, clique number, density, diameter, domination number, edge connectivity, genus, girth, group size, independence number, index, laplacian largest eigenvalue, longest induced cycle, longest induced path, matching number, maximum degree, minimum degree, number of components, number of edges, number of spanning trees, number of triangles, number of vertex orbits, number of vertices, number of zero eigenvalues, radius, second largest eigenvalue, smallest eigenvalue, treewidth, vertex connectivity

and allows you to restrict to any of these 11 graph classes:

• Acyclic, bipartite, claw-free, connected, Eulerian, Hamiltonian, hypohamiltonian, hypotraceable, planar, regular, traceable

Further, graphs can be drawn or uploaded (using any of their 6 supported formats).

As of Jan 2024 the database contained over 50,000 graphs.

• House of Graphs
• Gunnar Brinkmann, Kris Coolsaet, Jan Goedgebeur, and Hadrien Melot, House of Graphs: a database of interesting graphs (2012). arXiv:1204.3549 (math.CO; cs.DM)
• G. Brinkmann, K. Coolsaet, J. Goedgebeur, H. Mélot, House of Graphs: a database of interesting graphs, Discrete Applied Mathematics, 161(1-2):311-314, 2013. Available at https://houseofgraphs.org
• K. Coolsaet, Sven D'hondt and J. Goedgebeur, House of Graphs 2.0: a database of interesting graphs and more, Discrete Applied Mathematics, 325:97-107, 2023. Available at https://houseofgraphs.org

List of projects: topology

π-Base

James Dabbs' collections of counterexamples in topology. As of Jan 2024 it contains 171 spaces, 174 properties, and 405 theorems. It allows complex Boolean queries and is designed for automated deduction. Work goes back to at least 2013; Steven Clontz joined in 2017.

• π-Base
• GitHub project

List of projects: geometry

Encyclopedia of Triangle Centers

By Clark Kimberling. As of Jan 2024 it has over 60,000 triangle centers.

• Encyclopedia of Triangle Centers (ETC)

A Catalog of Lattices

A catalog of about 160,000 lattices for sphere packing by Gabriele Nebe and Neil Sloane.

• A Catalog of Lattices

List of projects: other

Reverse Mathematics Zoo

A database of reverse mathematical implications, conservation facts, and reducibilities, especially in the big five subsystems of second order arithmetic: RCA₀, WKL₀, ACA₀, ATR₀, and Π$\scriptstyle _{1}^{1}$-CA₀. It was developed Damir Dzhafarov and has been recently rewritten by Eric Astor.

• Reverse Mathematics Zoo
• Source code on GitHub

Encyclopedia of Delay-Insensitive Systems (EDIS)

Delay-insensitive systems operate correctly regardless of delays in components and connections. For each entry, information may include

1. Specifications, both informal and in various formalisms (XDI Model, VERDECT, DI Algebra).
2. Properties, such as symmetries (structural and behavioral automorphisms), classifications (kind of choice or nondeterminism involved), independent environments, etc.
3. Implementations, DI decompositions, and gate and/or transistor designs where relevant
4. Generalizations
5. Miscellaneous, such as associated problems and conjectures, historic notes, etc.
6. References

It appears to contain several dozen entries and has a last-modified date of 1998.

• Encyclopedia of Delay-Insensitive Systems (EDIS)

A Collection of Algebraic Identities

Tito Piezas III's collection of algebraic identities. Seems to have been last updated in 2010, and now it's dropped off the web. It is described as almost 300 pages and is divided into 14 parts and 31 sections (plus updates and an introduction).

• A Collection of Algebraic Identities (archive.org)

Other communities

• Mersenneforum.org
• factorize_request subreddit