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Strongly asymmetric sequences generated by four elements


Author: František Fiala
Journal: Math. Comp. 25 (1971), 155-162
MSC: Primary 05B30
DOI: https://doi.org/10.1090/S0025-5718-1971-0291113-6
MathSciNet review: 0291113
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Abstract: Some general properties of strongly asymmetric sequences generated by $ m \geqq 1$ elements (m-SAS) are given. Computational experience with two algorithms--for listing of all 4-SASs of a given length n and for generating the smallest 4-SAS of length $ n = 1,2, \cdots $ --supports the conjecture that there exists an infinite 4-SAS. The smallest 4-SAS of length 592 is presented.


References [Enhancements On Off] (What's this?)

  • [1] Erdös, "Some unsolved problems," Magyar Tud. Akad. Mat. Kutató Int. Közl., v. 6, 1961, pp. 221-254; Russian transl., Matematika, v. 7, 1963, no. 4, p. 128. MR 31 #2106. MR 0177846 (31:2106)
  • [2] A. A. Evdokimov, "Strongly asymmetric sequences generated by a finite number of symbols," Dokl. Akad. Nauk SSSR, v. 179, 1968, pp. 1268-1271 = Soviet Math. Dokl., v. 9, 1968, pp. 536-539. MR 38 #3156. MR 0234842 (38:3156)

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1971-0291113-6
Keywords: Strongly asymmetric sequences, lexicographical ordering, number systems
Article copyright: © Copyright 1971 American Mathematical Society

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