Literature cited
J. Steiner, “Combinatorische Aufgage, ” J. Reien und Angew. Math.,45, 181–182 (1853).
E. H. Moore, “Concerning triple systems, ” Math. Ann.,43, 271–285 (1893).
M. Reiss, “Uber eiene Steinersche combinatorische Aufgabe welche in 45sten Bande dieses journals, Seite 181, gestellt worden ist, ” J. Reine und Angew. Math.,56, 326–344 (1859).
T. P. Kirkman, “On a problem in combinations, ” Cambr. and Dublin Math. J.2, 191–204 (1847).
E. Netto, “Zur Theorie der Triplesysteme, ” Math. Ann.,42, 143–152 (1892).
K. Zulauf, Uber Tripelsysteme von 13 Elemente, Diss., Marburg (1897).
V. De Pasquale, “Sui sistemi ternari di 13 elementi, ” Rendiconti R. Instituto Lombardo, Ser.2, 32 (1899).
M. G. Brunel, “Sur le deux systemes de triades le treize elements, ” J. Mathematiques, Ser. 5, 7 (1901).
F. N. Cole, “The triad systems of thirteen letters, ” Trans. Amer. Math. Soc.,14, No. 1, 1–5 (1913).
F. N. Cole, L. D. Cummings, and H. S. White, “ The complete enumeration of triad systems in 15 elements,” Proc. Nat. Acad. Sci.,3, No. 3, 197–199 (1917).
Th. Skolem, “Some remarks on the Triple systems of Steiner, ” Math. Scand.,6, 273–280 (1958).
H. Hanani, “A note on Steiner triple systems,” Math. Scand.,8, 154–165 (1960).
A. J. W. Hilton, “On Steiner and similar triple systems,” Math. Scand.,24, 208–216 (1969).
A. Rosa, “Steiner triple systems and their chromatic number,” Acta Fac. Rerum Natur. Univ. Comen. Math.,24, 159–174 (1970).
L. D. Cummings “On a method of comparison for triple systems, ” Trans. Amer. Math. Soc.,15, 311–327 (1914).
H. S. White, L. D. Cummings, and F. N. Cole, “Complete classification of triad systems on fifteen elements,” Mem. Nat. Acad. Sci. USA,14, Second Memoir, 1–89 (1925).
J. Doyen, “Sur la structure de certains systems triples de Steiner,” Math. Z.,111, No. 4, 289–300 (1969).
M. Hall, Combinatorics [Russian translation], Mir (1970).
C. Treash, “A method of obtaining Steiner triple systems, ” Annals New York Acad. Sci.,175, No. 1, 338–384 (1970).
A. Ya. Petrenyuk, “On nonisomorphic principal Steiner triple systems and systems of pair groups,” Kibernetika, No. 4 (1971).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 24, No. 6, pp. 772–780, November–December, 1972.
The author thanks K. A. Rybnikov for his considerable interest in the work and his daily assistance.
Rights and permissions
About this article
Cite this article
Petrenyuk, A.Y. Tests for nonisomorphic Steiner triple systems. Ukr Math J 24, 620–626 (1972). https://doi.org/10.1007/BF01085412
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01085412