“Davenport-Schinzel Sequence”的概念、定义、习题解题方法及翻译-数学辞典

单词

Davenport-Schinzel Sequence

释义

Davenport-Schinzel Sequence

Form a sequence from an Alphabet of letters such that there are no consecutive letters and no alternatingsubsequences of length greater than . Then the sequence is a Davenport-Schinzel sequence if it has maximal length. The value of is the trivial sequence of 1s: 1, 1, 1, ... (Sloane's A000012). The values of are the A000027). The values of are theA005408). The first nontrivial Davenport-Schinzel sequence is given by 1, 4, 8, 12, 17, 22, 27, 32, ... (Sloane's A002004). Additional sequences are given by Guy (1994, p. 221) and Sloane.

References

Davenport, H. and Schinzel, A. ``A Combinatorial Problem Connected with Differential Equations.'' Amer. J. Math. 87, 684-690, 1965.

Guy, R. K. ``Davenport-Schinzel Sequences.'' §E20 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 220-222, 1994.

Roselle, D. P. and Stanton, R. G. ``Results of Davenport-Schinzel Sequences.'' In Proc. Louisiana Conference on Combinatorics, Graph Theory, and Computing. Louisiana State University, Baton Rouge, March 1-5, 1970 (Ed. R. C. Mullin, K. B. Reid, and D. P. Roselle). Winnipeg, Manitoba: Utilitas Mathematica, pp. 249-267, 1960.

Sharir, M. and Agarwal, P. Davenport-Schinzel Sequences and Their Geometric Applications. New York: Cambridge University Press, 1995.

Sloane, N. J. A. SequencesA000012/M0003,A000027/M0472,A002004/M3328, andA002004/M2400in ``An On-Line Version of the Encyclopedia of Integer Sequences.''http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S.The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.

随便看

数学辞典收录了8975条数学词条，基本涵盖了常用数学知识及数学英语单词词组的翻译及用法，是数学学习的有利工具。