PermPAL is an online database of permutation pattern avoidance classes and the enumerations.

**Cited or mentioned in:**

- A bijection for length-5 patterns in permutations. Joanna N. Chen and Zhicong Lin. Journal of Combinatorial Theory, Series A (2024)
- On permutation patterns with constrained gap sizes. Stoyan Dimitrov. Australasian Journal of Combinatorics (2023)

Open-source Python library to construct and manipulate several kinds of finite state machines.

Open-source Maple package to empirically predict the asymptotic behavior of counting sequences based on known initial terms.

**Cited or mentioned in:**

- Counting 3-stack-sortable permutations. Colin Defant. Journal of Combinatorial Theory, Series A (2020)
- Limiting probabilities for vertices of a given rank in 1-2 trees. Miklós Bóna and István Mező. Electronic Journal of Combinatorics (2019)
- Phase Coexistence for the Hard-Core Model on \(\mathbb{Z}^2\). Antonio Blanca, Yuxuan Chen, David Galvin, Dana Randall, and Prasad Tetali. Combinatorics, Probability, and Computing. (2018)
- Asymptotics of the number of standard Young tableaux of skew shape. Alejandro Morales, Igor Pak and Greta Panova. European Journal of Combinatorics (2018)

Open-source Maple package to conjecture generating functions of counting sequences based on known initial terms.

**Cited or mentioned in:**

- Algebraic and arithmetic properties of the cogrowth sequence of nilpotent group. Igor Pak and David Soukup. arXiv (2022)
- Factorization of Ising correlations C(M,N) for ν=-k and M+N odd, M ≤ N, T < T_c and their lambda extensions. S. Boukraa, C. Cosgrove, J.-M. Maillard, and B. M. McCoy. Journal of Physics A (2022)
- Symmetries of Non-Linear ODEs: Lambda Extensions of the Ising Correlations. S. Boukraa and J.-M. Maillard. Symmetry (2022)
- Counting 3-stack-sortable permutations. Colin Defant. Journal of Combinatorial Theory, Series A (2020)
- The Ising correlation C(M,N) for ν=-k. S. Boukraa, J.-M. Maillard, and B. M. McCoy. Journal of Physics A (2020)
- Three friendly walkers. Iwan Jensen. Journal of Physics A: Mathematical and Theoretical (2017)

with Christian Bean, Émile Nadeau, and Henning Ulfarsson

https://github.com/PermutaTriangle/comb_spec_searcher

https://github.com/PermutaTriangle/Tilings

https://github.com/PermutaTriangle/comb_spec_searcher

https://github.com/PermutaTriangle/Tilings

Open-source Python libraries that implement the combinatorial exploration framework and apply it to the field of permutation patterns.

**Cited or mentioned in:**

- A bijection for length-5 patterns in permutations. Joanna N. Chen and Zhicong Lin. Journal of Combinatorial Theory, Series A (2024)
- Composable Constraint Models for Permutation Enumeration. Ruth Hoffmnn, Özgür Akgün, and Christopher Jefferson. arXiv (2023)
- On the generating functions of pattern-avoiding Motzkin paths. Christian Bean, Antonio Bernini, Luca Ferrari, and Matteo Cervetti. Journal of Symbolic Computation (2022)
- Combinatorial specifications for juxtapositions of permutation classes. Robert Brignall and Jakub Sliačan. Electronic Journal of Combinatorics (2019)

with many contributors

https://github.com/PermutaTriangle/Permuta

https://github.com/PermutaTriangle/Permuta

Open-source Python library for working with permutations and patterns. Successor (in part) to PermPy. Co-authored with many other contributors.

**Cited or mentioned in:**

- Pattern-avoiding modified ascent sequences. Giulio Cerbai. arXiv (2024)
- Composable Constraint Models for Permutation Enumeration. Ruth Hoffmnn, Özgür Akgün, and Christopher Jefferson. arXiv (2023)
- Griddings of permutations and hardness of pattern matching. Vít Jelínek, Michal Opler, and Jakub Perkárek. Leibniz International Proceedings in Informatics (2021)
- Asymptotic behaviour of the containment of certain mesh patterns. Dejan Govc and Jason P. Smith. Discrete Mathematics (2022)

A web-based application to manage a worldwide distributed computational effort to compute the shortest superpermutation containing all permutations of length 6. Over a million computers participated in this effort and over a hundred million CPU-hours were contributed.

with Micheal Engen and Cheyne Homberger

https://github.com/engenmt/permpy

https://github.com/engenmt/permpy

PermPy is an open-source Python library for handling large sets of permutations.

**Cited or mentioned in:**

- Pattern avoidance for Fibonacci sequences using \(k\)-regular words. Emily Downing, Elizabeth J. Hartung, and Aaron Williams. arXiv (2023)
- K-polynomials of multiplicity-free varieties. Federico Castillo, Yairon Cid-Ruiz, Fatemeh Mohammadi, and Jonathan Montaño. arXiv (2022)
- Statistics on almost-Fibonacci pattern-avoiding permutations. Brody Lynch and Yihan Qin. Minnesota Journal of Undergraduate Mathematics (2022)
- Pattern avoidance in permutations and their squares. Miklós Bóna and Rebecca Smith. Discrete Mathematics (2019)
- A counterexample regarding labelled well-quasi-ordering. Robert Brignall, Michael Engen, and Vincent Vatter. Graphs and Combinatorics (2018)
- Fast algorithms for finding pattern avoiders and counting pattern occurrences in permutations. William Kuszmaul. Mathematics of Computation (2018)