@article{10_21136_CMJ_1970_100989,
author = {Schwarz, \v{S}tefan},
title = {On the semigroup of binary relations on a finite set},
journal = {Czechoslovak Mathematical Journal},
pages = {632--679},
year = {1970},
volume = {20},
number = {4},
doi = {10.21136/CMJ.1970.100989},
mrnumber = {0296190},
zbl = {0228.20034},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1970.100989/}
}
TY - JOUR AU - Schwarz, Štefan TI - On the semigroup of binary relations on a finite set JO - Czechoslovak Mathematical Journal PY - 1970 SP - 632 EP - 679 VL - 20 IS - 4 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1970.100989/ DO - 10.21136/CMJ.1970.100989 LA - en ID - 10_21136_CMJ_1970_100989 ER -
Schwarz, Štefan. On the semigroup of binary relations on a finite set. Czechoslovak Mathematical Journal, Tome 20 (1970) no. 4, pp. 632-679. doi: 10.21136/CMJ.1970.100989
[1] A. R. Bednarek A. D. Wallace: Some theorems on P-intersective sets. Acta Math. Acad. Sci. Hungaricae, 17 (1966), 9-14. | DOI | MR
[2] A. R. Bednarek A. D. Wallace: Finite approximants of compact totally disconnected machines. Mathematical Systems Theory 1 (1967), 209-216. | DOI | MR
[3] X. M. Девадзе: Порождающие множества некоторых подполугрупп полугруппы всех бинарных отношений в конечном множестве. Уч. зап. Ленинград, гос. пед. ин-та им. А. И. Геруена 387 (1968), 92-100. | MR | Zbl
[4] Р. Dubreill: Algèbre. (2 ed.), Paris (Gauthier-Villars), 1954.
[5] A. L. Dulmage, N. S. Mendelsohn: The exponent of a primitive matrix. Canad. Math. Bull. 5 (1962), 241-244. | DOI | MR | Zbl
[6] A. L. Dulmage, N. S. Mendelsohn: Gaps in the exponent set of primitive matrices. Illinois J. of Math. 8 (1964), 642-656. | DOI | MR | Zbl
[7] A. L. Dulmage, N. S. Mendelsohn: The structure of powers of non-negative matrices. Canad. J. of Math. 17 (1965), 318-330. | DOI | MR | Zbl
[8] A. L. Dulmage D. M. Johnson N. S. Mendelsohn: Connectivity and reducibility of graphs. Canad. J. of Math. 14 (1962), 529-539. | DOI | MR
[9] G. Frobenius: Über Matrizen aus nichtnegativen Elementen. S. В. Preuss. Akad. Wiss. 23 (1912), 456-477.
[10] Л. M. Глускин: Автоморфизмы полугрупп бинарных отношений. Мат. зап. Урале, гос. унив., Свердловск 6 (1967), 44-54. | MR | Zbl
[11] В. R. Heap, M. S. Lynn: The index of primitivity of a non-negative matrix. Numer. Math. 6 (1964), 120-141. | DOI | MR | Zbl
[12] B. R. Heap, M. S. Lynn: The structure of powers of non-negative matrices I. The index of convergence. SIAM J. of Appl. Math. 14 (1966), 610-639. | DOI | MR
[13] B. R. Heap, M. S. Lynn: The structure of powers of non-negative matrices II. The index of maximum density. Ibidem 14 (1966), 762-777. | MR
[14] J. С Holladay, R. S. Varga: On powers of non-negative matrices. Proc. Amer. Math. Soc. 9 (1958), 631-634. | DOI | MR | Zbl
[15] Ю. И. Любич: Оценки для оптимальной детерминизации недетерминированных автономных автоматов. Сибирск. мат. ж. 5 (1964), 337-355. | MR | Zbl
[16] М. Marcus, F. May: The maximum number of zeros in powers of an indecomposable matrix. Duke Math. J. 29 (1962), 581-588. | MR
[17] O. Ore: Theory of graphs. Amer. Math. Soc. Coll. Publ. Vol. 38, Providence, 1962. | Zbl
[18] P. Perkins: A theorem on regular matrices. Pacific J. of Math. 11 (1961), 1529-1533. | DOI | MR | Zbl
[19] V. Pták: On a combinatorial theorem and its application to non-negative matrices. Czech. Math. J. 8 (1958), 487-495. | MR
[20] N. Pullman: On the number of positive entries in the powers of a non-negative matrix. Canad. Math. Bull. 7 (1964), 525-537. | DOI | MR | Zbl
[21] J. Riguet: Relations binaires, fermeture, correspondences de Galois. Bull. Soc. Math. France 76 (1948), 114-155. | DOI | MR
[22] D. Rosenblatt: On the graphs and asymptotic forms of finite boolean relation matrices and stochastic matrices. Naval Res. Logist. Quarterly 4 (1957), 151-167. | DOI | MR
[23] Š. Schwarz: A semigroup treatment of some theorems on non-negative matrices. Czech. Math. J. 15 (1965), 212-229. | MR | Zbl
[24] Š. Schwarz: On powers of non-negative matrices. Mat.-fyz. časopis Slov. Akad. vied 15 (1965), 215-228. | MR | Zbl
[25] Š. Schwarz: Заметка к теории неотрицательных матриц. Сибирск. мат. ж. 6 (1965), 207-211. | MR | Zbl
[26] Š. Schwarz: A new approach to some problems in the theory of non-negative matrices. Czech. Math. J. 16 (1966), 274-284. | MR | Zbl
[27] Š. Schwarz: Some estimates in the theory of non-negative matrices. Czech. Mat. J. 17 (1967), 399-407. | MR | Zbl
[28] Š. Schwarz: New kinds of theorems on non-negative matrices. Czech. Math. J. 16 (1966), 285-295. | MR
[29] Š. Schwarz: On the index of imprimitivity of a non-negative matrix. Acta Scientiarum, Szeged, 28 (1967), 185-189. | MR | Zbl
[30] Š. Schwarz: On idempotent relations on a finite set. Czech. Math. J. 20 (1970), 696-702. | MR
[31] Š. Schwarz: On a sharp estimation in the theory of binary relations on a finite set. Czech. Math. J. 20 (1970), 703-714. | MR | Zbl
[32] Shinnousuke Aharu: A note on the powers of Boolean matrices. Proc. Japan Academy 43 (1967), 624-628. | MR
[33] Б. M. Шайн: Представление полугрупп при помощи бинарных отношений. Мат. сборник 60 (1963), 293-303. | MR | Zbl
[34] Б. М. Шайн: О некоторых классах полугрупп бинарных отношений. Сиб. мат. журнал 6 (1965), 616-635. | MR | Zbl
[35] Б. М. Шайн: Алгебры отношений. Межвузовский научный симпосиум по общей алгебре, Тарту 1966, 130-168. | Zbl
[36] В. В. Вагнер: Теория отношений и алгебра частичных отображений. Теория полугрупп и ее приложения. (Сборник статей). Саратов 1965, 3-178. | Zbl
[37] R. S. Varga: Matrix iterative analysis. New Jersey (Prentice-Hall), 1962. | MR
[38] A. D. Wallace: Relations on topological spaces. Proc. of Symp. in General Topology and its Relations to Modern Analysis and Algebra. Publishing House of the Czechoslovak Academy of Sciences. Prague, 1962, 356-360. | MR | Zbl
[39] A. D. Wallace: Relation theory. (Mimeographed lecture notes, Univ. of Florida.)
[40] H. Wielandt: Unzerlegbare, nicht negative Matrizen. Math. Z. 52 (1950), 575-583. | DOI | MR | Zbl
[41] К. A. Зарецкий: Абстрактная характеристика полугруппы всех бинарных отношений. Уч. зап. Ленинград, гос. пед, ин-та им. Герцена 183 (1958), 251-253. | Zbl
[42] К. А. Зарецкий: Регуларные элементы полугруппы бинарных отношений. Усп. мат. наук, XVII, вып. 3 (105) (1962), 177-179. | Zbl
[43] К. А. Зарецкий: Полугруппа бинарных отношений. Мат. сборник 61 (1963), 291 - 305. | MR | Zbl
[44] S. I. Montague, R. I. Plemmons: Maximal subgroups of the semigroup of relations. J. of Algebra, 13 (1969), 575-587. | DOI | MR | Zbl
[45] R. I. Plemmons, M. T. West: On the semigroup of binary relations. (To appear.) | Zbl
Cité par Sources :