| Title:
|
On the semigroup of binary relations on a finite set (English) |
| Author:
|
Schwarz, Štefan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
20 |
| Issue:
|
4 |
| Year:
|
1970 |
| Pages:
|
632-679 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| MSC:
|
04A20 |
| MSC:
|
05A05 |
| MSC:
|
20M20 |
| idZBL:
|
Zbl 0228.20034 |
| idMR:
|
MR0296190 |
| DOI:
|
10.21136/CMJ.1970.100989 |
| . |
| Date available:
|
2008-06-09T13:48:54Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/100989 |
| . |
| Reference:
|
[1] A. R. Bednarek A. D. Wallace: Some theorems on P-intersective sets.Acta Math. Acad. Sci. Hungaricae, 17 (1966), 9-14. MR 0189999, 10.1007/BF02020438 |
| Reference:
|
[2] A. R. Bednarek A. D. Wallace: Finite approximants of compact totally disconnected machines.Mathematical Systems Theory 1 (1967), 209-216. MR 0222869, 10.1007/BF01703819 |
| Reference:
|
[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. Zbl 1171.62301, MR 0232871 |
| Reference:
|
[4] Р. Dubreill: Algèbre.(2 ed.), Paris (Gauthier-Villars), 1954. |
| Reference:
|
[5] A. L. Dulmage, N. S. Mendelsohn: The exponent of a primitive matrix.Canad. Math. Bull. 5 (1962), 241-244. Zbl 0108.01203, MR 0142566, 10.4153/CMB-1962-023-2 |
| Reference:
|
[6] A. L. Dulmage, N. S. Mendelsohn: Gaps in the exponent set of primitive matrices.Illinois J. of Math. 8 (1964), 642-656. Zbl 0125.00706, MR 0181645, 10.1215/ijm/1256059464 |
| Reference:
|
[7] A. L. Dulmage, N. S. Mendelsohn: The structure of powers of non-negative matrices.Canad. J. of Math. 17 (1965), 318-330. Zbl 0196.30301, MR 0213384, 10.4153/CJM-1965-031-9 |
| Reference:
|
[8] A. L. Dulmage D. M. Johnson N. S. Mendelsohn: Connectivity and reducibility of graphs.Canad. J. of Math. 14 (1962), 529-539. MR 0140436, 10.4153/CJM-1962-044-0 |
| Reference:
|
[9] G. Frobenius: Über Matrizen aus nichtnegativen Elementen.S. В. Preuss. Akad. Wiss. 23 (1912), 456-477. |
| Reference:
|
[10] Л. M. Глускин: Автоморфизмы полугрупп бинарных отношений.Мат. зап. Урале, гос. унив., Свердловск 6 (1967), 44-54. Zbl 1103.35360, MR 0218474 |
| Reference:
|
[11] В. R. Heap, M. S. Lynn: The index of primitivity of a non-negative matrix.Numer. Math. 6 (1964), 120-141. Zbl 0121.26303, MR 0163921, 10.1007/BF01386062 |
| Reference:
|
[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. MR 0225671, 10.1137/0114052 |
| Reference:
|
[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 0225672 |
| Reference:
|
[14] J. С Holladay, R. S. Varga: On powers of non-negative matrices.Proc. Amer. Math. Soc. 9 (1958), 631-634. Zbl 0096.00805, MR 0097416, 10.1090/S0002-9939-1958-0097416-8 |
| Reference:
|
[15] Ю. И. Любич: Оценки для оптимальной детерминизации недетерминированных автономных автоматов.Сибирск. мат. ж. 5 (1964), 337-355. Zbl 1117.65300, MR 0162725 |
| Reference:
|
[16] М. Marcus, F. May: The maximum number of zeros in powers of an indecomposable matrix.Duke Math. J. 29 (1962), 581-588. MR 0150154 |
| Reference:
|
[17] O. Ore: Theory of graphs.Amer. Math. Soc. Coll. Publ. Vol. 38, Providence, 1962. Zbl 0105.35401 |
| Reference:
|
[18] P. Perkins: A theorem on regular matrices.Pacific J. of Math. 11 (1961), 1529-1533. Zbl 0103.00801, MR 0147420, 10.2140/pjm.1961.11.1529 |
| Reference:
|
[19] V. Pták: On a combinatorial theorem and its application to non-negative matrices.Czech. Math. J. 8 (1958), 487-495. MR 0110644 |
| Reference:
|
[20] N. Pullman: On the number of positive entries in the powers of a non-negative matrix.Canad. Math. Bull. 7 (1964), 525-537. Zbl 0143.26304, MR 0180562, 10.4153/CMB-1964-049-x |
| Reference:
|
[21] J. Riguet: Relations binaires, fermeture, correspondences de Galois.Bull. Soc. Math. France 76 (1948), 114-155. MR 0028814, 10.24033/bsmf.1401 |
| Reference:
|
[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. MR 0090910, 10.1002/nav.3800040206 |
| Reference:
|
[23] Š. Schwarz: A semigroup treatment of some theorems on non-negative matrices.Czech. Math. J. 15 (1965), 212-229. Zbl 0232.20139, MR 0175919 |
| Reference:
|
[24] Š. Schwarz: On powers of non-negative matrices.Mat.-fyz. časopis Slov. Akad. vied 15 (1965), 215-228. Zbl 0158.28302, MR 0191987 |
| Reference:
|
[25] Š. Schwarz: Заметка к теории неотрицательных матриц.Сибирск. мат. ж. 6 (1965), 207-211. Zbl 0232.20139, MR 0171791 |
| Reference:
|
[26] Š. Schwarz: A new approach to some problems in the theory of non-negative matrices.Czech. Math. J. 16 (1966), 274-284. Zbl 0232.20140, MR 0201452 |
| Reference:
|
[27] Š. Schwarz: Some estimates in the theory of non-negative matrices.Czech. Mat. J. 17 (1967), 399-407. Zbl 0159.32603, MR 0217101 |
| Reference:
|
[28] Š. Schwarz: New kinds of theorems on non-negative matrices.Czech. Math. J. 16 (1966), 285-295. MR 0201453 |
| Reference:
|
[29] Š. Schwarz: On the index of imprimitivity of a non-negative matrix.Acta Scientiarum, Szeged, 28 (1967), 185-189. Zbl 0232.15004, MR 0214610 |
| Reference:
|
[30] Š. Schwarz: On idempotent relations on a finite set.Czech. Math. J. 20 (1970), 696-702. MR 0268047 |
| Reference:
|
[31] Š. Schwarz: On a sharp estimation in the theory of binary relations on a finite set.Czech. Math. J. 20 (1970), 703-714. Zbl 0226.20061, MR 0282862 |
| Reference:
|
[32] Shinnousuke Aharu: A note on the powers of Boolean matrices.Proc. Japan Academy 43 (1967), 624-628. MR 0223382 |
| Reference:
|
[33] Б. M. Шайн: Представление полугрупп при помощи бинарных отношений.Мат. сборник 60 (1963), 293-303. Zbl 1145.93303, MR 0153760 |
| Reference:
|
[34] Б. М. Шайн: О некоторых классах полугрупп бинарных отношений.Сиб. мат. журнал 6 (1965), 616-635. Zbl 1099.01519, MR 0193170 |
| Reference:
|
[35] Б. М. Шайн: Алгебры отношений.Межвузовский научный симпосиум по общей алгебре, Тарту 1966, 130-168. Zbl 1155.78304 |
| Reference:
|
[36] В. В. Вагнер: Теория отношений и алгебра частичных отображений. Теория полугрупп и ее приложения.(Сборник статей). Саратов 1965, 3-178. Zbl 1099.01519 |
| Reference:
|
[37] R. S. Varga: Matrix iterative analysis.New Jersey (Prentice-Hall), 1962. MR 0158502 |
| Reference:
|
[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. Zbl 0114.14303, MR 0146788 |
| Reference:
|
[39] A. D. Wallace: Relation theory.(Mimeographed lecture notes, Univ. of Florida.) |
| Reference:
|
[40] H. Wielandt: Unzerlegbare, nicht negative Matrizen.Math. Z. 52 (1950), 575-583. Zbl 0035.29101, MR 0035265, 10.1007/BF02230720 |
| Reference:
|
[41] К. A. Зарецкий: Абстрактная характеристика полугруппы всех бинарных отношений.Уч. зап. Ленинград, гос. пед, ин-та им. Герцена 183 (1958), 251-253. Zbl 0995.62501 |
| Reference:
|
[42] К. А. Зарецкий: Регуларные элементы полугруппы бинарных отношений.Усп. мат. наук, XVII, вып. 3 (105) (1962), 177-179. Zbl 1005.68507 |
| Reference:
|
[43] К. А. Зарецкий: Полугруппа бинарных отношений.Мат. сборник 61 (1963), 291 - 305. Zbl 1145.93303, MR 0155785 |
| Reference:
|
[44] S. I. Montague, R. I. Plemmons: Maximal subgroups of the semigroup of relations.J. of Algebra, 13 (1969), 575-587. Zbl 0184.03703, MR 0252539, 10.1016/0021-8693(69)90119-7 |
| Reference:
|
[45] R. I. Plemmons, M. T. West: On the semigroup of binary relations.(To appear.) Zbl 0208.01801 |
| . |
