Skip to main content
Log in

Combinatorial properties of binary semigroups

  • Published:
Periodica Mathematica Hungarica Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. P. S. Aleksandrov,Combinatorial Topology, Vol. 1, Graylock, Rochester, N. Y., 1956.

    Google Scholar 

  2. J. Baillieul, Green's relations in finite function semigroups,Aequationes Math. 7 (1971), 22–27.

    Article  Google Scholar 

  3. C. Bass andK. K.-H. Butler, Combinatorial properties of partial transformation semigroups, unpublished, 1972.

  4. G. Birkhoff,Lattice Theory, Amer. Math. Soc., Providence, R. I., 1967.

    Google Scholar 

  5. R. L. Brandon, K. K.-H. Butler, D. W. Hardy andG. Markowsky, Cardinalities ofD-classes inB n,Semigroup Forum 4 (1972), 341–344.

    Google Scholar 

  6. K. K.-H. Butler,On (0, 1)-matrix semigroups, Dissertation, The George Washington University, Washington, D. C., 1971.

    Google Scholar 

  7. , On (0, 1)-matrix semigroups,Semigroup Forum 3 (1971), 74–79.

    Google Scholar 

  8. , The number of idempotents in (0, 1)-matrix semigroups,Linear Algebra and Appl. 5 (1972), 233–246.

    Article  Google Scholar 

  9. , The number of partially ordered sets,J. Combinatorial Theory Ser. B 13 (1972), 276–289.

    Article  Google Scholar 

  10. ,The number of partial order graphs, Lecture Notes in Math., No. 303, Springer-Verlag, Berlin—Heidelberg—New York, 1972, 55–63.

    Google Scholar 

  11. K. K.-H. Butler andG. Markowsky, The number of solutions ofA 2=0, unpublished, 1972.

  12. , Partially ordered and quasi-ordered sets,Notices Amer. Math. Soc. 19 (1972), A-563.

    Google Scholar 

  13. K. K.-H. Butler, Canonical bijection betweenD-classes of (0, 1)-matrix semigroups,Period. Math. Hungar. 4 (1973), 303–305.

    Article  Google Scholar 

  14. D. Cartwright, F. Harary andR. Z. Norman,Structure Models, Wiley, New York, 1965.

    Google Scholar 

  15. A. H. Clifford, A proof of the Montague-Plemmons-Schein Theorem on maximal subgroups of the semigroup of binary relations,Semigroup Forum 1 (1970), 272–275.

    Google Scholar 

  16. andD. D. Miller, Union and symmetry preserving endomorphisms of the semigroup of all binary relations on a set,Czechoslovak Math. J. 20 (1970), 303–314.

    Google Scholar 

  17. andG. B. Preston,The Algebraic Theory of Semigroups, Vol. 1, Amer. Math. Soc., Providence, R. I., 1961.

    Google Scholar 

  18. ,The Algebraic Theory of Semigroups, Vol. 2, Amer. Math. Soc., Providence, R. I., 1967.

    Google Scholar 

  19. R. L. Davis, The number of structures of finite relations,Proc. Amer. Math. Soc. 4 (1953), 486–494.

    Google Scholar 

  20. J. Dénes, On transformations, transformation-semigroups and graphs,Proc. Colloq. Graph Theory, Tihany, 1966, 65–75.

  21. , Some combinatorial properties of transformations and their connections with the theory of graphs,J. Combinatorial Theory 9 (1970), 108–116.

    Google Scholar 

  22. C. G. Doss,Certain equivalence relations in transformation semigroups, M. A. Thesis, Directed by D. D. Miller, Univ. of Tenn., Knowville, Tenn., 1955.

    Google Scholar 

  23. P. Dubreil,Algèbre, 2nd edition, Gauthier-Villars, Paris, 1954.

    Google Scholar 

  24. J. W. Evans, F. Harary andM. S. Lynn, On the computer enumeration of finite topologies,Comm. ACM 10 (1967), 295–298.

    Article  Google Scholar 

  25. L. M. Gluskin, Semigroups of transformations (autoreferat of the doctoral dissertation),Uspehi Mat. Nauk 17 (106) (1962), 233–240 (in Russian).

    Google Scholar 

  26. , Ideals of transformation semigroups,Mat. Sb. 47 (1959), 111–130 (in Russian).

    Google Scholar 

  27. , Ideals of semigroups,Mat. Sb. 55 (1961), 421–448 (in Russian).

    Google Scholar 

  28. , Transitive semigroups of transformations,Dokl. Akad. Nauk SSSR 129 (1959), 16–18 (in Russian).

    Google Scholar 

  29. E. S. Ljapin, Associative systems of all partial transformations,Dokl. Akad. Nauk. SSSR 88 (1953), 13–15 (errata92 (1953), 692) (in Russian).

    Google Scholar 

  30. , Abstract characteristic of certain semigroups of transformations,Leningrad. Gos. Ped. Inst. Učen. Zap. 103 (1955), 5–30 (in Russian).

    Google Scholar 

  31. , On representations of semigroups by partial transformations,Mat. Sb. 52 (1960), 589–596 (in Russian).

    Google Scholar 

  32. B. Harris, A note on the number of idempotent elements in symmetric semigroups, MRC Tech. Rpt. 699, Math. Res. Ctr., Univ. of Wisconsin, Nov. 1966.

  33. andL. Schoenfeld, The number of idempotent elements in symmetric semigroups,J. Combinatorial Theory 3 (1967), 122–135.

    Google Scholar 

  34. , Automorphisms of the semigroup of all relations on a set,Canad. Math. Bull. 9 (1966), 73–77.

    Google Scholar 

  35. , Zero-free fortifying homomorphisms and semigroups of relations,Bull. Austral. Math. Soc. 1 (1969), 213–230.

    Google Scholar 

  36. G. Markowsky, Green's equivalence relations and the semigroup of binary relations on a set, unpublished, 1972.

  37. , Idempotents and product representations with applications to the semigroup of binary relations,Semigroup Forum 5 (1972), 95–119.

    Google Scholar 

  38. C. J. Maxon, On semigroups of Boolean ring endomorphisms,Semigroup Forum 4 (1972), 78–82.

    Google Scholar 

  39. S. I. Montague andR. I. Plemmons, Maximal subgroups of the semigroup of relations,J. Algebra 13 (1969), 575–587.

    Article  Google Scholar 

  40. M. Petrich,Topics in Semigroups, Lecture Note, Penn. State Univ., University Park, Penn., 1967.

    Google Scholar 

  41. , Translational hull and semigroups of binary relations,Glasgow Math. J. 9 (1968), 12–21.

    Google Scholar 

  42. R. J. Plemmons andB. M. Schein, Groups of binary relations,Semigroup Forum 1 (1970), 267–271.

    Google Scholar 

  43. R. J. Plemmons andM. West, On the semigroup of binary relations,Pacific J. Math. 35 (1970), 743–753.

    Google Scholar 

  44. J. Riguet, Relations binaires, fermeture, correspondences de Galois,Bull. Soc. Math. France 76 (1948), 114–155.

    Google Scholar 

  45. J. Riordan,An Introduction to Combinatorial Analysis, Wiley, New York, 1958.

    Google Scholar 

  46. D. Rosenblatt, On the graphs and asymptotic forms of finite Boolean relation matrices and stochastic matrices,Naval Res. Logist. Quart. 4 (1957), 151–167.

    Google Scholar 

  47. H. Sharp, Cardinality of finite topologies,J. Combinatorial Theory 5 (1968), 82–86.

    Google Scholar 

  48. B. M. Schein, Relation algebras and function semigroups,Semigroup Forum 1 (1970), 1–62.

    Google Scholar 

  49. , Ordered sets, semilattices, distributive lattices and Boolean algebras with homomorphic endomorphism semigroups,Fund. Math. 68 (1970), 31–50.

    Google Scholar 

  50. B. M. Schein, Representation of semigroups, First All-Union Sympos. Theory of Semigroups, Sverdlovsk, (1969), 79–89 (in Russian).

  51. S. Schwarz, On the semigroup of binary relations on a finite set,Czechoslovak Math. J. 20 (1970), 632–679.

    Google Scholar 

  52. , On idempotent relations on a finite set,Czechoslovak Math. J. 20 (1970), 696–702.

    Google Scholar 

  53. , On a sharp estimation in the theory of binary relations on a finite set,Czechoslovak Math. J. 20 (1970), 703–714.

    Google Scholar 

  54. M. Tainiter, A characterization of idempotents in semigroups,J. Combinatorial Theory 5 (1968), 370–373.

    Google Scholar 

  55. V. V. Vagner, Generalized groups,Dokl. Akad. Nauk SSSR 84 (1952), 1119–1122 (MR 14-12).

    Google Scholar 

  56. J. A. Wright, Cycle indices of certain classes of quasiorder types or topologies, Private communication, 1972.

  57. M. Yoeli, A note on a generalization of Boolean matrix theory,Amer. Math. Monthly 68 (1961), 552–557.

    Google Scholar 

  58. K. A. Zaretskii, Abstract characteristic of the semigroup of all binary relations,Leningrad. Gos. Ped. Inst. Učen. Zap. 183 (1958), 252–263 (in Russian).

    Google Scholar 

  59. , Semigroup of binary relations,Mat. Sb. 61 (1963), 291–305 (in Russian).

    Google Scholar 

  60. , Regular elements in the semigroup of binary relations,Uspehi Mat. Nauk 17 (1962), 177–179 (in Russian).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to my parents Mr. and Mrs.Jin-Gyong Kim of Number 435 Yongdam-Ri, Yonghawa-Myon, Anjoo-Goon, Pyongan-Namdo, North Korea and to my adopted parents Mr. and Mrs.Decature P. Butler of McCall Creek, Mississippi 39647, U.S.A.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ki-Hang Butler, K. Combinatorial properties of binary semigroups. Period Math Hung 5, 3–46 (1974). https://doi.org/10.1007/BF02018162

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02018162

Keywords

Navigation