Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
Generating trees and the Catalan and Schro¨der numbers
Discrete Mathematics
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Generating trees and proper Riordan arrays
Discrete Mathematics
Mixed succession rules: The commutative case
Journal of Combinatorial Theory Series A
Algebraic aspects of some Riordan arrays related to binary words avoiding a pattern
Theoretical Computer Science
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In this paper we study the enumeration and the construction of particular binary words avoiding the pattern 1j+10j. By means of the theory of Riordan arrays, we solve the enumeration problem and we give a particular succession rule, called jumping and marked succession rule, which describes the growth of such words according to their number of ones. Moreover, the problem of associating a word to a path in the generating tree obtained by the succession rule is solved by introducing an algorithm which constructs all binary words and then kills those containing the forbidden pattern.