We consider some Riordan arrays related to binary words avoiding a pattern which can be easily studied by means of an A-matrix rather than their A-sequence. Both concepts allow us to define every element as a linear combination of other elements in the array; the A-sequence is unique while the A-matrix is not. However, for the problems considered in the present paper, we show that the A-matrix approach is more convenient. We provide explicit algebraic generating functions for these Riordan arrays and obtain many statistics on the corresponding languages.
Algebraic aspects of some Riordan arrays related to binary words avoiding a pattern / D. Merlini; R. Sprugnoli. - STAMPA. - (2009), pp. 1-11. (Intervento presentato al convegno 7th International Conference on Words, WORDS 2009 tenutosi a Salerno, Italy nel September 14-18, 2009).
Algebraic aspects of some Riordan arrays related to binary words avoiding a pattern
MERLINI, DONATELLA;SPRUGNOLI, RENZO
2009
Abstract
We consider some Riordan arrays related to binary words avoiding a pattern which can be easily studied by means of an A-matrix rather than their A-sequence. Both concepts allow us to define every element as a linear combination of other elements in the array; the A-sequence is unique while the A-matrix is not. However, for the problems considered in the present paper, we show that the A-matrix approach is more convenient. We provide explicit algebraic generating functions for these Riordan arrays and obtain many statistics on the corresponding languages.
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