Discrete Applied Mathematics - Special volume: combinatorics and theoretical computer science
Riordan arrays and combinatorial sums
Discrete Mathematics
An introduction to the analysis of algorithms
An introduction to the analysis of algorithms
Compact recognizers of episode sequences
Information and Computation
Journal of the ACM (JACM)
Analytic Combinatorics
Enumerative Combinatorics: Volume 1
Enumerative Combinatorics: Volume 1
Pattern 1 j+10 j Avoiding Binary Words
Fundamenta Informaticae - Lattice Path Combinatorics and Applications
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We consider some Riordan arrays related to binary words avoiding a pattern p, 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 and corresponds to a linear dependence from the previous row. The A-matrix is not unique and corresponds to a linear dependence from several previous rows. 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. We thus obtain a deeper insight of the languages L^[^p^] of binary words avoiding p having a number of 0s less or equal to the number of 1s.