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# 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.

## Contents

- 1 Properties
- 2 List of projects
- 2.1 On-Line Encyclopedia of Integer Sequences
- 2.2 Database of Permutation Pattern Avoidance
- 2.3 The Combinatorial Statistic Finder
- 2.4 Hypergeometric series / WZ method / A = B
- 2.5 House of Graphs
- 2.6 RIES
- 2.7 Inverse Symbolic Calculator
- 2.8 gfun
- 2.9 SequenceBoss
- 2.10 Groupprops
- 2.11 Integer Sequences
- 2.12 The Number Fields Database
- 2.13 A Database for Number Fields
- 2.14 L-functions and modular forms database
- 2.15 π-Base
- 2.16 Reverse Mathematics Zoo

- 3 Other communities
- 4 Notes

## Properties

Billey & Tenner's^{[1]} *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

### On-Line Encyclopedia of Integer Sequences

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

### 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 48 entries as of Oct 2015. 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.

### 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 2015 there were 285 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.

### House of Graphs

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

The database allows searches by text and any of these 23 graph invariants:

- Acyclic?; algebraic connectivity; average degree; bipartite?; chromatic index; chromatic number; claw-free?; clique number; connected?; diameter; edge connectivity; Eulerian?; genus; girth; Hamiltonian?; independence number; index; Laplacian largest eigenvalue; longest induced cycle; longest induced path; matching number; maximum degree; minimum degree; minimum dominating set; number of components; number of edges; number of triangles; number of vertices; radius; regular?; second largest eigenvalue; smallest eigenvalue; vertex connectivity

with a given value or in a given interval (except the binary properties, marked with a ? in this list, which can be only present or absent).

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

As of Oct 2015 the database contained 8766 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)

### 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.

### 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)

### SequenceBoss

A relatively new (2015) project by Philipp Emanuel Weidmann. Accepts sequence queries.

- SequenceBoss
- sequencer on github

### 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)

### 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.

### 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.

- 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)

### 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.

### π-Base

James Dabbs' collections of counterexamples in topology. As of January 2016 it contains 159 spaces, 94 properties, and 214 theorems. It allows complex Boolean queries and is designed for automated deduction. Work goes back to at least 2013.

### Reverse Mathematics Zoo

A database of reverse mathematical implications, conservation facts, and reducibilities, especially in the big five subsystems of second order arithmetic: RCA_{0}, WKL_{0}, ACA_{0}, ATR_{0}, and Π-CA_{0}. It was developed Damir Dzhafarov and has been recently rewritten by Eric Astor.

## Other communities

## Notes

- ↑ Sara C. Billey; Bridget E. Tenner. "Fingerprint databases for theorems".
*Notices of the AMS***60**(8): pp. 1034–1039. arXiv:1304.3866 .