Algorithms for Producing and Ordering Lexical and Nonlexical Sequences out of One Element

作者：Abboud Elias^*

来源：Annals of Combinatorics, 2011, 15(1): 1-17.

DOI：10.1007/s00026-011-0079-4

• elementary operations
• splitting of a cell
• conjugation of a cell
• lexical sequences
• adjacent

This paper deals with algorithms for producing and ordering lexical and nonlexical sequences of a given degree. The notion of "elementary operations" on positive alpha-sequences is introduced. Our main theorem answers the question of when two lexical sequences are adjacent. Given any lexical sequence, alpha is an element of 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 alpha' is an element of L(n), then compute the fundamental sequence f = alpha <^> alpha' is an element of L(m) and conclude for m inverted iota n that a is adjacent to alpha' in L(n). Whereas for m | n, the sequence a is adjacent to a sequence generated by f and the least element of L(d), where d = n/m. Thus, while right sequences control the lexicality property of an alpha-sequence, it turns out that left sequences control the adjacency property of lexical and nonlexical sequences.

• 出版日期2011-3