An Asymptotic Series for the Number of Three-Line Latin Rectangles

Koichi YAMAMOTO

doi:10.2969/jmsj/00140226

Koichi YAMAMOTO

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ジャーナルフリー

1950 年 1 巻 4 号 p. 226-241

DOI https://doi.org/10.2969/jmsj/00140226

詳細

Published: 1950 Received: 1948/12/10 Available on J-STAGE: 2006/08/29 Accepted: - Advance online publication: - Revised: -
訂正情報
訂正日: 2006/08/29 訂正理由: - 訂正箇所: 引用文献情報訂正内容: Wrong : 1) The author has not yet access to this paper.
2) In this country, M. Takasaki obtained a recursive formula for f(n, 3), involving three other rows of numbers. But it was sterile for asymptotic behaviors.
3) The presence of this term was pointed out by Prof. Kawada.
4) This estimation is undoubtedly too crude. I believe it should be reduced to_??_ Cn! With some constant C, but I cannot prove.
5) See e.g. N. Wiener: The Fourier integral and certain of its applications, Cambridge. 1933, p. 54.
6) H. Poincaré: Sur les equations linéaires aux differetielles ordinaires et aux differences finies. Amer. J. Math. 7 (1885), pp. 1-56=Oeuvres, t. I, Paris 1928, pp. 226-289.
7) H. Poincaré: loc. cit., paragraph VII.
8) I owe this form of the proposition to Prof. Kawada.
9) I have computed these values through Takasaki's formula, and verified by Riordan's formula ([2] and [3]).

Right : 1) The author has not yet access to this paper.
2) In this country, M. Takasaki obtained a recursive formula for f (n, 3), involving three other rows of numbers. But it was sterile for asymptotic behaviors.
4) The presence of this term was pointed out by Prof. Kawada.
5) This estimation is undoubtedly too crude. I believe it should be reduced to ≤Cn! with some constant C, but I cannot prove.
6) See e. g. N. Wiener: The Fourier integral and certain of its applications, Cambridge. 1933, p. 54.
7) H. Poincaré: Sur les equations linéaires aux differetielles ordinaires et aux differences finies. Amer. J. Math. 7 (1885), pp. 1-56=Oeuvres, t. I, Paris 1928, pp. 226-289.
8) H. Poincaré: loc. cit., paragraph VII.
9) I owe this form of the proposition to Prof. Kawada.
10) I have computed these values through Takasaki's formula, and verified by Riordan's formula ([2] and [3]).

訂正日: 2006/08/29 訂正理由: - 訂正箇所: PDFファイル訂正内容: -

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