Bibliography¶
A. Abram and C. Reutenauer. The stylic monoid. Semigroup Forum, 105(1):1–45, 2022. doi:10.1007/s00233-022-10285-3.
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.
Robert E. Arthur and N. Ruškuc. 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.
Colin M. Campbell, Edmund F. Robertson, Nikola Ruškuc, 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.
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.
Olexandr Ganyushkin and Volodymyr Mazorchuk. Classical Finite Transformation Semigroups. Springer London, 2009. doi:10.1007/978-1-84800-281-4.
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.
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/.
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. 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.
E. H. Moore. Concerning the abstract groups of order k!, k!/2, ... Proc. London Math. Soc., 1(28):357–366, 1897.
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 Ruškuc. Semigroup presentations. PhD thesis, University of St Andrews, 1995. URL: https://research-repository.st-andrews.ac.uk/handle/10023/2821.
Charles C. Sims. Computation with finitely presented groups. Encyclopedia of mathematics and its applications. Cambridge University Press, Cambridge„ England, New York, 1994. ISBN 0-521-43213-8. URL: http://opac.inria.fr/record=b1082972.