caa a22 4500 44585555X CHVBK 20180317145427.0 cr unu---uuuuu 170323e20110301xx s 000 0 eng 10.1007/s00026-011-0079-4 doi (NATIONALLICENCE)springer-10.1007/s00026-011-0079-4 Abboud Elias Beit Berl College, 44905, Doar Beit Berl, Israel aut Algorithms for Producing and Ordering Lexical and Nonlexical Sequences out of One Element [Elektronische Daten] [Elias Abboud] This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations” on positive α-sequences is introduced. Our main theorem answers the question of when two lexical sequences are adjacent. Given any lexical sequence, α ∈ L n, 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′ ∈ L n, then compute the fundamental sequence $${f = \alpha \wedge \alpha\prime \in L_{m}}$$ and conclude for $${m \nmid n}$$ that α is adjacent to α′ in L n. Whereas for m | n, the sequence α is adjacent to a sequence by f and the least element of L d, where $${{d = \frac{n}{m}}}$$. 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. Springer Basel AG, 2011 elementary operations nationallicence splitting of a cell nationallicence conjugation of a cell nationallicence lexical sequences nationallicence adjacent nationallicence Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 1-17 0218-0006 15:1<1 2011 15 26 https://doi.org/10.1007/s00026-011-0079-4 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00026-011-0079-4 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Abboud Elias Beit Berl College, 44905, Doar Beit Berl, Israel aut NATIONALLICENCE 773 0- Annals of Combinatorics SP Birkhäuser Verlag Basel 15/1(2011-03-01), 1-17 0218-0006 15:1<1 2011 15 26 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer