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 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 --supports the conjecture that there exists an infinite 4-SAS. The smallest 4-SAS of length 592 is presented.

**[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