Bibliography
A. Abram and C. Reutenauer. The stylic monoid. Semigroup Forum, 105(1):1–45, 2022. doi:10.1007/s00233-022-10285-3.
Antoine Abram, Florent Hivert, James D. Mitchell, Jean-Christophe Novelli, and Maria Tsalakou. Power quotients of plactic-like monoids. 06 2024. doi:10.4204/EPTCS.403.7.
Alfred V. Aho and Margaret J. Corasick. Efficient string matching: an aid to bibliographic search. Communications of the ACM, 18(6):333–340, June 1975. URL: https://doi.org/10.1145/360825.360855 (visited on 2024-03-26), doi:10.1145/360825.360855.
A. Aizenstat. Defining relations of finite symmetric semigroups. Mat. Sb. N.S., 45(87):261–280, 1958.
A. Aizenstat. Generating relations of an endomorphism semigroup of a finite linearly ordered chain. Sibirsk. Mat. Z., 2:9–11, 1962.
Marina Anagnostopoulou-Merkouri, James D. Mitchell, and Maria Tsalakou. Computing the congruences of a finite semigroup or monoid. 2023. URL: https://arxiv.org/abs/2302.06295, doi:10.48550/ARXIV.2302.06295.
Robert E. Arthur and N. Ruskuc. Presentations for two extensions of the monoid of order-preserving mappings on a finite chain. Southeast Asian Bulletin of Mathematics, 24(1):1–7, 2000. doi:10.1007/s10012-000-0001-1.
H. Ayik, C. M. Campbell, J. J. O'Connor, and N. Ruskuc. Minimal presentations and efficiency of semigroups. Semigroup Forum, 60(2):231–242, 2000. doi:10.1007/s002339910016.
William Burnside. Theory of Groups of Finite Order. Cambridge University Press, 2012. doi:10.1017/cbo9781139237253.023.
C. M. Campbell and E. F. Robertson. A deficiency zero presentation for sl(2, p). Bulletin of the London Mathematical Society, 12:17–20, 1980. doi:10.1112/blms/12.1.17.
Colin M. Campbell, Edmund F. Robertson, Nikola Ruskuc, and Richard M. Thomas. Fibonacci semigroups. Journal of Pure and Applied Algebra, 94(1):49–57, 1994. URL: https://doi.org/10.1016/0022-4049(94)90005-1, doi:10.1016/0022-4049(94)90005-1.
Robert D. Carmichael. Introduction To The Theory Of Groups Of Finite Order. Dover Publications, 1956.
Vincent Carnino and Sven De Felice. Random Generation of Deterministic Acyclic Automata Using Markov Chains, pages 65–75. Springer Berlin Heidelberg, 2011. URL: http://dx.doi.org/10.1007/978-3-642-22256-6_7, doi:10.1007/978-3-642-22256-6_7.
Julien Cassaigne, Marc Espie, Daniel Krob, Jean-Christophe Novelli, and Florent Hivert. The chinese monoid. International Journal of Algebra and Computation, 11(03):301–334, 2001. URL: https://doi.org/10.1142/S0218196701000425, doi:10.1142/s0218196701000425.
T. D. H. Coleman, J. D. Mitchell, F. L. Smith, and M. Tsalakou. The todd-coxeter algorithm for semigroups and monoids. 2022. arXiv:arXiv:2203.11148.
H. S. M. Coxeter and W. O. J. Moser. Generators and relators for discrete groups. Springer-Verlag, 1979.
David Easdown, James East, and D. G. FitzGerald. A presentation for the dual symmetric inverse monoid. 2007. doi:10.48550/arxiv.0707.2439.
James East. Generators and relations for partition monoids and algebras. Journal of Algebra, 339(1):1–26, 2011. doi:10.1016/j.jalgebra.2011.04.008.
James East. Presentations for Temperley–Lieb Algebras. The Quarterly Journal of Mathematics, 72(4):1253–1269, 02 2021. URL: https://doi.org/10.1093/qmath/haab001, doi:10.1093/qmath/haab001.
Vitor Hugo Fernandes. On the cyclic inverse monoid on a finite set. 2022. doi:10.48550/ARXIV.2211.02155.
Vítor H. Fernandes and Tânia Paulista. On the monoid of partial isometries of a cycle graph. 2022. doi:10.48550/ARXIV.2205.02196.
D.G. FitzGerald. A presentation for the monoid of uniform block permutations. Bulletin of the Australian Mathematical Society, 68(2):317–324, 2003. doi:10.1017/s0004972700037692.
Véronique Froidure and Jean-Eric Pin. Algorithms for computing finite semigroups. In Foundations of computational mathematics (Rio de Janeiro, 1997), pages 112–126. Springer, Berlin, 1997.
Harold N. Gabow. Path-based depth-first search for strong and biconnected components. Information Processing Letters, 74(34):107 – 114, 2000. URL: https://www.sciencedirect.com/science/article/pii/S002001900000051X, doi:https://dx.doi.org/10.1016/S0020-0190(00)00051-X.
Olexandr Ganyushkin and Volodymyr Mazorchuk. Classical Finite Transformation Semigroups. Springer London, 2009. doi:10.1007/978-1-84800-281-4.
Joël Gay. Representation of Monoids and Lattice Structures in the Combinatorics of Weyl Groups. Theses, Université Paris Saclay (COmUE), June 2018. URL: https://theses.hal.science/tel-01861199.
Joël Gay and Florent Hivert. The 0-rook monoid and its representation theory. October 2019. URL: https://doi.org/10.48550/arXiv.1910.11740.
Robert H Gilman. Presentations of groups and monoids. Journal of Algebra, 57(2):544–554, April 1979.
Eddy Godelle. A note on renner monoids. 2009. URL: https://arxiv.org/abs/0904.0926, doi:10.48550/arxiv.0904.0926.
R. M Guralnick, W. M Kantor, M. Kassabov, and A. Lubotzky. Presentations of finite simple groups: a quantitative approach. Journal of the American Mathematical Society, 21:711–774, 2008. doi:10.1090/S0894-0347-08-00590-0.
Tom Halverson and Arun Ram. Partition algebras. European Journal of Combinatorics, 26:869–921, 2005. doi:10.1016/j.ejc.2004.06.005.
George Havas and Colin Ramsay. Coset enumeration: ACE. PhD thesis, University of Queensland, 1999.
Derek Holt. Kbmag – GAP package, Version 1.5.9. July 2019. URL: https://gap-packages.github.io/kbmag/.
John E. Hopcroft and R. M. Karp. A linear algorithm for testing equivalence of finite automata. December 1971. URL: https://hdl.handle.net/1813/5958.
Nagayoshi Iwahori and Nobuko Iwahori. On a set of generating relations of the full transformation semigroups. Journal of Combinatorial Theory, Series A, 16(2):147–158, 1974. URL: https://www.sciencedirect.com/science/article/pii/0097316574900405, doi:https://doi.org/10.1016/0097-3165(74)90040-5.
Matthias Jantzen. Confluent string rewriting. Volume 14. Springer Science & Business Media, 2012.
Julius Jonusas, James D. Mitchell, and Markus Pfeiffer. Two variants of the Froidure-Pin algorithm for finite semigroups. Port. Math., 74(3):173–200, 2017. URL: https://doi.org/10.4171/PM/2001, doi:10.4171/pm/2001.
Mark Kambites. Small overlap monoids. II. Automatic structures and normal forms. J. Algebra, 321(8):2302–2316, 2009. URL: http://dx.doi.org/10.1016/j.jalgebra.2008.12.028, doi:10.1016/j.jalgebra.2008.12.028.
Mark Kambites. Small overlap monoids. I. The word problem. J. Algebra, 321(8):2187–2205, 2009. URL: http://dx.doi.org/10.1016/j.jalgebra.2008.09.038, doi:10.1016/j.jalgebra.2008.09.038.
Donald E. Knuth. Permutations, matrices, and generalised young tableaux. Pacific Journal of Mathematics, 34(3):709–727, 1970. doi:10.2140/pjm.1970.34.709.
Donald E. Knuth. The Art of Computer Programming, Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams. Addison-Wesley Professional, 12th edition, 2009. ISBN 0321580508, 9780321580504.
Janusz Konieczny. Green's equivalences in finite semigroups of binary relations. Semigroup Forum, 48(2):235–252, 1994. doi:10.1007/bf02573672.
Ganna Kudryavtseva and Volodymyr Mazorchuk. On presentations of brauer-type monoids. Central European Journal of Mathematics, 2007. doi:10.2478/s11533-006-0017-6.
Gerard Lallement and Robert McFadden. On the determination of Green's relations in finite transformation semigroups. J. Symbolic Comput., 10(5):481–498, 1990. doi:10.1016/s0747-7171(08)80057-0.
Alain Lascoux and Marcel-P. Schützenberger. Le monoïde plaxique. In Noncommutative structures in algebra and geometric combinatorics (Naples, 1978), volume 109 of Quad. “Ricerca Sci.”, pages 129–156. CNR, Rome, 1981.
Victor Maltcev and Volodymyr Mazorchuk. Presentation of the singular part of the brauer monoid. Mathematica Bohemica, 2007. doi:10.21136/mb.2007.134125.
Paul Martin and Volodymyr Mazorchuk. Partitioned binary relations. 2011. URL: https://arxiv.org/abs/1102.0862, arXiv:1102.0862.
Paul Martin and Volodymyr Mazorchuk. Partitioned binary relations. Mathematica Scandinavica, 113(1):30–52, 2013. URL: http://www.jstor.org/stable/24493105.
J. D. Mitchell and M. Tsalakou. An explicit algorithm for normal forms in small overlap monoids. preprint, 2021.
James D. Mitchell and Murray T. Whyte. Short presentations for transformation monoids. 06 2024. URL: https://arxiv.org/abs/2406.19294.
E. H. Moore. Concerning the abstract groups of order k!, k!/2, ... Proc. London Math. Soc., 1(28):357–366, 1897.
Jean-Christophe Novelli. On the hypoplactic monoid. Discrete Mathematics, 217(1):315–336, 2000. URL: https://www.sciencedirect.com/science/article/pii/S0012365X99002708, doi:https://doi.org/10.1016/S0012-365X(99)00270-8.
Eliezer Posner, Kris Hatch, and Megan Ly. Presentation of the motzkin monoid. 01 2013. URL: https://arxiv.org/abs/1301.4518.
J. Radoszewski and W. Rytter. Efficient testing of equivalence of words in a free idempotent semigroup. In SOFSEM 2010: Theory and Practice of Computer Science, 663–671. 01 2010. doi:10.1007/978-3-642-11266-9_55.
Nikola Ruskuc. Semigroup presentations. PhD thesis, University of St Andrews, 1995. URL: https://research-repository.st-andrews.ac.uk/handle/10023/2821.
É. G. Shutov. Defining relations in finite semigroups of partial transformations. Sov. Math., Dokl., 1:784–786, 1960.
Charles C. Sims. Computation with Finitely Presented Groups. Encyclopedia of Mathematics and its Applications. Cambridge University Press, 1994. URL: https://doi.org/10.1017/CBO9780511574702.
Joseph Buchanan Stephen. Applications of automata theory to presentations of monoids and inverse monoids. ETD collection for University of Nebraska-Lincoln, 01 1987. URL: https://digitalcommons.unl.edu/dissertations/AAI8803771.