



@article{ Radoszewski2010aa,
  author =           {Radoszewski, J. and Rytter, W.},
  editor =           {van  Leeuwen,  J.  and  Muscholl, A. and Peleg, D. and
                      Pokorn{\a'y}, J. and Rumpe, B.},
  title =            {Efficient  Testing  of  Equivalence of Words in a Free
                      Idempotent Semigroup},
  journal =          {SOFSEM 2010: Theory and Practice of Computer Science},
  publisher =        {Springer Berlin Heidelberg},
  address =          {Berlin, Heidelberg},
  year =             {2010},
  pages =            {663\texttt{\symbol{45}}\texttt{\symbol{45}}671},
  isbn =             {978\texttt{\symbol{45}}3\texttt{\symbol{45}}642\texttt{\symbol{45}}11266\texttt{\symbol{45}}9},
  doi =              {doi.org/10.1007/978\texttt{\symbol{45}}3\texttt{\symbol{45}}642\texttt{\symbol{45}}11266\texttt{\symbol{45}}9{\textunderscore}55},
  printedkey =       {RR10}
}
@article{ Donoven2018aa,
  author =           {Donoven, C. and Mitchell, J. D. and Wilson, W. A.},
  title =            {Computing maximal subsemigroups of a finite semigroup},
  journal =          {Journal of Algebra},
  month =            {July},
  volume =           {505},
  year =             {2018},
  pages =            {559\texttt{\symbol{45}}596},
  doi =              {doi.org/10.1016/j.jalgebra.2018.01.044},
  eprint =           {1606.05583},
  printedkey =       {DMW18}
}
@article{ East2019aa,
  author =           {East, J.},
  title =            {Presentations  for rook partition monoids and algebras
                      and their singular ideals},
  journal =          {J. Pure and Applied Algebra},
  month =            {March},
  volume =           {223},
  year =             {2019},
  pages =            {1097\texttt{\symbol{45}}1122},
  url =              {https://www.sciencedirect.com/science/article/pii/S0022404918301403},
  issue =            {3},
  printedkey =       {Eas19}
}
@article{ Grood2006aa,
  author =           {Grood, C.},
  title =            {The rook partition algebra},
  journal =          {J. Combin. Theory Ser. A},
  volume =           {113},
  number =           {2},
  year =             {2006},
  pages =            {325{\textendash}351},
  issn =             {0097\texttt{\symbol{45}}3165},
  url =              {https://dx.doi.org/10.1016/j.jcta.2005.03.006},
  doi =              {10.1016/j.jcta.2005.03.006},
  printedkey =       {Gro06}
}
@article{ Kudryavtseva2015aa,
  author =           {Kudryavtseva, G. and Maltcev, V. and Umar, A.},
  title =            {Presentation  for  the  partial dual symmetric inverse
                      monoid},
  journal =          {Comm. Algebra},
  volume =           {43},
  number =           {4},
  year =             {2015},
  pages =            {1621{\textendash}1639},
  issn =             {0092\texttt{\symbol{45}}7872},
  url =              {https://dx.doi.org/10.1080/00927872.2013.876031},
  doi =              {10.1080/00927872.2013.876031},
  printedkey =       {KMU15}
}
@article{ Kudryavtseva2011aa,
  author =           {Kudryavtseva, G. and Maltcev, V.},
  title =            {Two   generalisations   of   the   symmetric   inverse
                      semigroups},
  journal =          {Publ. Math. Debrecen},
  volume =           {78},
  number =           {2},
  year =             {2011},
  pages =            {253{\textendash}282},
  issn =             {0033\texttt{\symbol{45}}3883},
  url =              {https://dx.doi.org/10.5486/PMD.2011.4375},
  doi =              {10.5486/PMD.2011.4375},
  printedkey =       {KM11}
}
@inproceedings{ JunttilaKaski,
  author =           {Junttila, T. and Kaski, P.},
  editor =           {Applegate,  D.  and  Brodal, G. S. and Panario, D. and
                      Sedgewick, R.},
  booktitle =        {Proceedings   of   the  Ninth  Workshop  on  Algorithm
                      Engineering and Experiments and the Fourth Workshop on
                      Analytic Algorithms and Combinatorics},
  title =            {Engineering  an  efficient canonical labeling tool for
                      large and sparse graphs},
  publisher =        {SIAM},
  year =             {2007},
  pages =            {135{\textendash}149},
  printedkey =       {JK07}
}
@article{ Martin2011aa,
  author =           {Martin, P. and Mazorchuk, V.},
  title =            {Partitioned binary relations},
  journal =          {Mathematica Scandinavica},
  volume =           {113},
  year =             {2013},
  pages =            {30\texttt{\symbol{45}}52},
  url =              {https://www.mscand.dk/article/view/15480},
  doi =              {https://doi.org/10.7146/math.scand.a\texttt{\symbol{45}}15480},
  printedkey =       {MM13}
}
@manual{ Pin2009aa,
  author =           {Pin, J.\texttt{\symbol{45}}E.},
  title =            {Semigroupe  2.01:  a  software  for  computing  finite
                      semigroups},
  organization =     {Laboratoire  d'Informatique Algorithmique : Fondements
                      et Applications (LIAFA), CNRS et Universit{\a'e} Paris
                      7},
  edition =          {2.01},
  year =             {2009},
  printedkey =       {Pin09}
}
@incollection{ Froidure1997aa,
  author =           {Froidure, V. and Pin, J.\texttt{\symbol{45}}E.},
  booktitle =        {Foundations  of  computational  mathematics  ({R}io de
                      {J}aneiro, 1997)},
  title =            {Algorithms for computing finite semigroups},
  publisher =        {Springer},
  address =          {Berlin},
  year =             {1997},
  pages =            {112{\textendash}126},
  printedkey =       {FP97}
}
@article{ Mitchell2019aa,
  author =           {East,  J.  and  Egri\texttt{\symbol{45}}Nagy,  A.  and
                      Mitchell, J. D. and P{\a'e}resse, Y.},
  title =            {Computing finite semigroups},
  journal =          {J. Symbolic Computation},
  volume =           {92},
  year =             {2019},
  pages =            {110 \texttt{\symbol{45}} 155},
  url =              {https://www.sciencedirect.com/science/article/pii/S0747717118300087},
  doi =              {https://doi.org/10.1016/j.jsc.2018.01.002},
  printedkey =       {EEMP19}
}
@article{ Gabow2000aa,
  author =           {Gabow, H. N.},
  title =            {Path\texttt{\symbol{45}}based
                      depth\texttt{\symbol{45}}first  search  for strong and
                      biconnected components},
  journal =          {Information Processing Letters},
  volume =           {74},
  number =           {3\texttt{\symbol{45}}4},
  year =             {2000},
  pages =            {107 \texttt{\symbol{45}} 114},
  issn =             {0020\texttt{\symbol{45}}0190},
  url =              {https://www.sciencedirect.com/science/article/pii/S002001900000051X},
  keywords =         {Algorithms},
  doi =              {https://dx.doi.org/10.1016/S0020\texttt{\symbol{45}}0190(00)00051\texttt{\symbol{45}}X},
  printedkey =       {Gab00}
}
@article{ Araujo2015aa,
  author =           {Ara{\a'u}jo,  J. and Bentz, W. and Mitchell, J. D. and
                      Schneider, C.},
  title =            {The   rank   of   the   semigroup  of  transformations
                      stabilising a partition of a finite set},
  journal =          {Math. Proc. Camb. Phil. Soc.},
  volume =           {159},
  year =             {2015},
  pages =            {339 \texttt{\symbol{45}} 353},
  issue =            {2},
  printedkey =       {ABMS15}
}
@article{ Fitzgerald1998aa,
  author =           {Fitzgerald, D. G. and Leech, J.},
  title =            {Dual  symmetric  inverse  monoids  and  representation
                      theory},
  journal =          {J. Austral. Math. Soc. A},
  volume =           {64},
  year =             {1998},
  pages =            {345\texttt{\symbol{45}}67},
  keywords =         {imported},
  printedkey =       {FL98}
}
@article{ Graham1968aa,
  author =           {Graham, N. and Graham, R. and Rhodes, J.},
  title =            {Maximal subsemigroups of finite semigroups},
  journal =          {J. Combinatorial Theory},
  volume =           {4},
  year =             {1968},
  pages =            {203{\textendash}209},
  printedkey =       {GGR68}
}
@article{ Graham1968Graph,
  author =           {Graham, R.},
  title =            {On  finite  0\texttt{\symbol{45}}simple semigroups and
                      graph theory},
  journal =          {Mathematical systems theory},
  volume =           {2},
  number =           {4},
  year =             {1968},
  pages =            {325{\textendash}339},
  printedkey =       {Gra68}
}
@article{ Halverson2005PartitionAlgebras,
  author =           {Halverson, T. and Ram, A.},
  title =            {Partition algebras},
  journal =          {European Journal of Combinatorics},
  publisher =        {Elsevier},
  volume =           {26},
  number =           {6},
  year =             {2005},
  pages =            {869{\textendash}921},
  printedkey =       {HR05}
}
@article{ Schein1992aa,
  author =           {Schein, B. M.},
  title =            {The minimal degree of a finite inverse semigroup},
  journal =          {Trans. Amer. Math. Soc.},
  volume =           {333},
  number =           {2},
  year =             {1992},
  pages =            {877{\textendash}888},
  printedkey =       {Sch92}
}
@article{ Araujo2009aa,
  author =           {Ara{\a'u}jo, J. and Mitchell, J. D. and Schneider, C.},
  title =            {Groups  that together with any transformation generate
                      regular semigroups or idempotent generated semigroups},
  journal =          {Journal of Algebra},
  volume =           {343},
  year =             {2011},
  issue =            {1},
  printedkey =       {AMS11}
}
@article{ Kudryavtseva2009aa,
  author =           {Kudryavtseva, G. and Mazorchuk, V.},
  title =            {On {K}iselman's semigroup},
  journal =          {Yokohama Math. J.},
  volume =           {55},
  number =           {1},
  year =             {2009},
  pages =            {21{\textendash}46},
  printedkey =       {KM09}
}
@article{ Gray2008aa,
  author =           {Gray, R. and Mitchell, J. D.},
  title =            {Largest   subsemigroups  of  the  full  transformation
                      monoid},
  journal =          {Discrete Math.},
  volume =           {308},
  number =           {20},
  year =             {2008},
  pages =            {4801{\textendash}4810},
  printedkey =       {GM08}
}
@article{ Araujo2010aa,
  author =           {Ara{\a'u}jo,  J. and B{\"u}nau, P. V. and Mitchell, J.
                      D. and Neunh{\"o}ffer, M.},
  title =            {Computing automorphisms of semigroups},
  journal =          {J. Symbolic Computation},
  volume =           {45},
  number =           {3},
  year =             {2010},
  pages =            {373{\textendash}392},
  printedkey =       {ABMN10}
}
@article{ Lallement1990aa,
  author =           {Lallement, G. and McFadden, R.},
  title =            {On  the determination of {G}reen's relations in finite
                      transformation semigroups},
  journal =          {J. Symbolic Computation},
  volume =           {10},
  number =           {5},
  year =             {1990},
  pages =            {481{\textendash}498},
  issn =             {0747\texttt{\symbol{45}}7171},
  printedkey =       {LM90}
}
@article{ Linton2002aa,
  author =           {Linton,  S.  A.  and Pfeiffer, G. and Robertson, E. F.
                      and Ru{\v s}kuc, N.},
  title =            {Computing transformation semigroups},
  journal =          {J. Symbolic Computation},
  volume =           {33},
  number =           {2},
  year =             {2002},
  pages =            {145{\textendash}162},
  printedkey =       {LPRR02}
}
@article{ Linton1998aa,
  author =           {Linton,  S.  A.  and Pfeiffer, G. and Robertson, E. F.
                      and Ru{\v s}kuc, N.},
  title =            {Groups and actions in transformation semigroups},
  journal =          {Math. Z.},
  volume =           {228},
  number =           {3},
  year =             {1998},
  pages =            {435{\textendash}450},
  printedkey =       {LPRR98}
}
@book{ Howie1995aa,
  author =           {Howie, J. M.},
  title =            {Fundamentals of semigroup theory},
  publisher =        {The Clarendon Press Oxford University Press},
  series =           {London Mathematical Society Monographs. New Series},
  volume =           {12},
  address =          {New York},
  year =             {1995},
  pages =            {x+351},
  note =             {Oxford Science Publications},
  isbn =             {0\texttt{\symbol{45}}19\texttt{\symbol{45}}851194\texttt{\symbol{45}}9},
  printedkey =       {How95}
}
@article{ Gomes1992aa,
  author =           {Gomes, G. M. S. and Howie, J. M.},
  title =            {On    the    ranks    of    certain    semigroups   of
                      order\texttt{\symbol{45}}preserving transformations},
  journal =          {Semigroup Forum},
  volume =           {45},
  number =           {3},
  year =             {1992},
  pages =            {272{\textendash}282},
  issn =             {0037\texttt{\symbol{45}}1912},
  printedkey =       {GH92}
}
@article{ Arthur2000aa,
  author =           {Arthur, R. E. and Ruskuc, N.},
  title =            {Presentations  for  two  extensions  of  the monoid of
                      order\texttt{\symbol{45}}preserving   mappings   on  a
                      finite chain},
  journal =          {Southeast Asian Bull. Math.},
  volume =           {24},
  number =           {1},
  year =             {2000},
  pages =            {1{\textendash}7},
  issn =             {0129\texttt{\symbol{45}}2021},
  printedkey =       {AR00}
}
@article{ Mandel1977aa,
  author =           {Mandel A., S. I.},
  title =            {On Finite Semigroups of Matrices},
  journal =          {Theoretical Computer Science},
  volume =           {5},
  year =             {1977},
  pages =            {101{\textendash}111},
  printedkey =       {MA77}
}
@article{ Gaubert1996aa,
  author =           {Gaubert, S.},
  title =            {On   the   {B}urnside   problem  for  {S}emigroups  of
                      {M}atrices over the (max, +) {A}lgebra},
  journal =          {Semigroup Forum},
  volume =           {5},
  year =             {1996},
  pages =            {271\texttt{\symbol{45}}292},
  printedkey =       {Gau96}
}
@book{ Bacelli1992aa,
  author =           {Baccelli F. Cohen G. Olsder G. J., Q. J. P.},
  title =            {Synchronisation  and  {L}inearity:  An  {A}lgebra  for
                      {D}iscrete {E}vent {S}ystems},
  publisher =        {Wiley},
  year =             {1992},
  printedkey =       {BFCGOGJ92}
}
@mastersthesis{ Kacie2009aa,
  author =           {Farlow, K. G.},
  title =            {{Max\texttt{\symbol{45}}Plus Algebra}},
  school =           {Virginia   {P}olytechnic   {I}nstitute   and   {S}tate
                      {U}niversity},
  address =          {United States},
  year =             {2009},
  printedkey =       {Far09}
}
@mastersthesis{ Burrell2016aa,
  author =           {Burrell, S. A.},
  title =            {{The  Order  Problem  for  Natural and Tropical Matrix
                      Semigroups}},
  school =           {University of St Andrews},
  address =          {United Kingdom},
  year =             {2016},
  printedkey =       {Bur16},
  type =             {{MM}ath project}
}
@inproceedings{ Simon1978aa,
  author =           {Simon, I.},
  booktitle =        {Proceedings   of   the   19th   Annual   Symposium  on
                      Foundations of Computer Science},
  title =            {Limited Subsets of a Free Monoid},
  publisher =        {IEEE Computer Society},
  series =           {SFCS '78},
  address =          {Washington, DC, USA},
  year =             {1978},
  pages =            {143{\textendash}150},
  url =              {https://dx.doi.org/10.1109/SFCS.1978.21},
  doi =              {10.1109/SFCS.1978.21},
  printedkey =       {Sim78}
}
@article{ Johnson1975aa,
  author =           {Johnson, D. B.},
  title =            {Finding  all  the  elementary  circuits  of a directed
                      graph},
  journal =          {SIAM J. Comput.},
  volume =           {4},
  year =             {1975},
  pages =            {77\texttt{\symbol{45}}84},
  printedkey =       {Joh75}
}
@article{ auinger2012krohn,
  author =           {Auinger, K.},
  title =            {Krohn{\textendash}{R}hodes complexity of {B}rauer type
                      semigroups},
  journal =          {Portugaliae Mathematica},
  volume =           {69},
  number =           {4},
  year =             {2012},
  pages =            {341{\textendash}360},
  printedkey =       {Aui12}
}
@article{ Mesyan2016,
  author =           {Mesyan, Z. and Mitchell, J. D.},
  title =            {The structure of a graph inverse semigroup},
  journal =          {Semigroup Forum},
  month =            {March},
  publisher =        {Springer Nature},
  volume =           {93},
  number =           {1},
  year =             {2016},
  pages =            {111{\textendash}130},
  url =              {https://doi.org/10.1007/s00233\texttt{\symbol{45}}016\texttt{\symbol{45}}9793\texttt{\symbol{45}}x},
  doi =              {10.1007/s00233\texttt{\symbol{45}}016\texttt{\symbol{45}}9793\texttt{\symbol{45}}x},
  printedkey =       {MM16}
}
@article{ Brouwer2015aa,
  author =           {Brouwer, A. E. and Draisma, J. and Frenk, B. J.},
  title =            {Lossy Gossip and Composition of Metrics},
  journal =          {Discrete \& Computational Geometry},
  volume =           {53},
  number =           {4},
  year =             {2015},
  pages =            {890{\textendash}913},
  issn =             {1432\texttt{\symbol{45}}0444},
  url =              {https://dx.doi.org/10.1007/s00454\texttt{\symbol{45}}015\texttt{\symbol{45}}9666\texttt{\symbol{45}}1},
  doi =              {10.1007/s00454\texttt{\symbol{45}}015\texttt{\symbol{45}}9666\texttt{\symbol{45}}1},
  printedkey =       {BDF15}
}
@article{ Wang2019aa,
  author =           {Wang, Z.\texttt{\symbol{45}}P.},
  title =            {Congruences on Graph Inverse Semigroups},
  journal =          {Journal of Algebra},
  month =            {sep},
  publisher =        {Elsevier \texttt{\symbol{123}}BV\texttt{\symbol{125}}},
  volume =           {534},
  year =             {2019},
  pages =            {51\texttt{\symbol{45}}\texttt{\symbol{45}}64},
  url =              {https://doi.org/10.1016/j.jalgebra.2019.06.020},
  printedkey =       {Wan19}
}
@article{ Anagnostopoulou-Merkouri2021aa,
  author =           {Anagnostopoulou\texttt{\symbol{45}}Merkouri,   M.  and
                      Mesyan, Z. and Mitchell, J. D.},
  title =            {Properties  of  congruence  lattices  of graph inverse
                      semigroups},
  journal =          {International Journal of Algebra and Computation},
  year =             {2023},
  arxiv =            {2108.08277},
  printedkey =       {AMM23}
}
@article{ Petrich1968aa,
  author =           {Petrich, M.},
  title =            {The     translational    hull    of    a    completely
                      0\texttt{\symbol{45}}simple semigroup},
  journal =          {Glasgow Mathematical Journal},
  volume =           {9},
  number =           {1},
  year =             {1968},
  pages =            {1\texttt{\symbol{45}}\texttt{\symbol{45}}11},
  printedkey =       {Pet68}
}
@article{ Petrich1970aa,
  author =           {Petrich, M.},
  title =            {The translational hull in semigroups and rings},
  journal =          {Semigroup Forum},
  volume =           {1},
  number =           {1},
  year =             {1970},
  pages =            {283\texttt{\symbol{45}}\texttt{\symbol{45}}360},
  issn =             {1432\texttt{\symbol{45}}2137},
  url =              {https://doi.org/10.1007/BF02573051},
  doi =              {10.1007/BF02573051},
  printedkey =       {Pet70}
}
@article{ Clifford1977aa,
  author =           {Clifford, A. H. and Petrich, M.},
  title =            {Some classes of completely regular semigroups},
  journal =          {Journal of Algebra},
  volume =           {46},
  number =           {2},
  year =             {1977},
  pages =            {462\texttt{\symbol{45}}\texttt{\symbol{45}}480},
  issn =             {0021\texttt{\symbol{45}}8693},
  url =              {http://dx.doi.org/10.1016/0021\texttt{\symbol{45}}8693(77)90383\texttt{\symbol{45}}0},
  printedkey =       {CP77}
}
