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pascal triangles

discrete mathematics

riordan arrays

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catalan numbers

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Some history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
A survey on Riordan arrays
Donatella Merlini
Dipartimento di Sistemi e Informatica
Universit`a di Firenze, Italia
December 13, 2011, Paris
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
Outline
1 Some history
2 Main properties of Riordan arrays
3 Riordan arrays and binary words avoiding a pattern
4 Riordan arrays, combinatorial sums and recursive matrices
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
A previous seminar
I’m very sorry to have not met P. Flajolet in the recent years.
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
A previous seminar
I’m very sorry to have not met P. Flajolet in the recent years.
I remember with pleasure my seminar at INRIA on October
10, 1994: Riordan arrays and their applications
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
References -1-
1 D. G. Rogers. Pascal triangles, Catalan numbers and renewal
arrays. Discrete Mathematics, 22: 301–310, 1978.
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
References -1-
1 D. G. Rogers. Pascal triangles, Catalan numbers and renewal
arrays. Discrete Mathematics, 22: 301–310, 1978.
2 L. W. Shapiro, S. Getu, W.-J. Woan, and L. Woodson. The
Riordan group. Discrete Applied Mathematics, 34: 229–239,
1991.
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
References -1-
1 D. G. Rogers. Pascal triangles, Catalan numbers and renewal
arrays. Discrete Mathematics, 22: 301–310, 1978.
2 L. W. Shapiro, S. Getu, W.-J. Woan, and L. Woodson. The
Riordan group. Discrete Applied Mathematics, 34: 229–239,
1991.
3 R. Sprugnoli. Riordan arrays and combinatorial sums.
Discrete Mathematics, 132: 267–290, 1994.
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
References -1-
1 D. G. Rogers. Pascal triangles, Catalan numbers and renewal
arrays. Discrete Mathematics, 22: 301–310, 1978.
2 L. W. Shapiro, S. Getu, W.-J. Woan, and L. Woodson. The
Riordan group. Discrete Applied Mathematics, 34: 229–239,
1991.
3 R. Sprugnoli. Riordan arrays and combinatorial sums.
Discrete Mathematics, 132: 267–290, 1994.
4 D. Merlini, D. G. Rogers, R. Sprugnoli, and M. C. Verri. On
some alternative characterizations of Riordan arrays.
Canadian Journal of Mathematics, 49(2): 301–320, 1997.
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
References -2-
1 T. X. He and R. Sprugnoli. Sequence characterization of
Riordan arrays.Discrete Mathematics, 309: 3962–3974, 2009.
Donatella Merlini A survey on Riordan arraysSome history
Main properties of Riordan arrays
Riordan arrays and binary words avoiding a pattern
Riordan arrays, combinatorial sums and recursive matrices
References -2-
1 T. X. He and R. Sprugnoli. Sequence characterization of
Riordan arrays.Discrete Mathematics, 309: 3962–3974, 2009.
2 D. Merlini and R. Sprugnoli. Algebraic aspects of some
Riordan arrays related to binary words avoiding a pattern.
Theoretical Computer Science, 412 (27), 2988-3001, 2011.
Donatella Merlini A survey on Riordan arrays