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1-17 Algorithms for Producing and Ordering Lexical and Nonlexical Sequences out of One Element
Elias Abboud
Beit Berl College, Doar Beit Berl, 44905 Israel
eabboud@beitberl.ac.il
Annals of Combinatorics 15 (1) pp.1-17 January, 2011
AMS Subject Classification: 05A17, 68R15, 37B10
Abstract:
This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of  “elementary operations” on positive a-sequences is introduced. Our main theorem answers the question of when two lexical sequences are adjacent. Given any lexical sequence, α∈Ln; we can produce its adjacent successor as follows; apply one elementary operation on the tail of the longest left sequence, of even length, which gives a lexical successor α'∈Ln, then compute the fundamental sequence f = α ^ α'∈Lm and conclude for m n that a is adjacent to α' in Ln; ; . Whereas for m | n, the sequence α is adjacent to a sequence generated by f and the least element of Ld; where d = : Thus, while right sequences control the lexicality property of an α-sequence, it turns out that left sequences
control the adjacency property of lexical and nonlexical sequences.
Keywords: elementary operations, splitting of a cell, conjugation of a cell, lexical sequences, adjacent

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