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- Cristiano Corsani, Donatella Merlini, Renzo Sprugnoli
- Discrete Mathematics
- 1998

The inversion of combinatorial sums is a fundamental problem in algebraic combinatorics. Some combinatorial sums, such as a n = P k d n;k b k , can not be inverted in terms of the orthogonalityâ€¦ (More)

We give several new characterizations of Riordan Arrays, the most important of which is: if fd n;k g n;k2N is a lower triangular array whose generic element d n;k linearly depends on the elements inâ€¦ (More)

- Donatella Merlini, Renzo Sprugnoli, M. Cecilia Verri
- The American Mathematical Monthly
- 2007

can be found in closed form by means of certain transformations on generating functions and the extraction of coefficients (see the end of section 3) suggested by Ira Gessel, and they comment: â€œHeâ€¦ (More)

- Donatella Merlini, M. Cecilia Verri
- Discrete Mathematics
- 2000

16 other words, the ending point is not situated above the main diagonal x = y. When the path never goes above this diagonal, we simply call it an underdiagonal path. Shapiro's paths 8] are anotherâ€¦ (More)

- Donatella Merlini
- DRW
- 2003

In this paper we consider a model of random walks previously studied in [BM02]: each walk starts (at time 0) from a point p0 of and at time n, one makes a jump xn ; the new position is given by theâ€¦ (More)

- Donatella Merlini, Renzo Sprugnoli, M. Cecilia Verri
- Theor. Comput. Sci.
- 2000

We study the problem of tiling a rectangular pÃ— n-strip (pâˆˆN xed, nâˆˆN) with pieces, i.e., sets of simply connected cells. Some well-known examples are strip tilings with dimers (dominoes) and=orâ€¦ (More)

- Donatella Merlini, Renzo Sprugnoli, M. Cecilia Verri
- CAAP
- 1994

Proof. The rst identity derives from Theorem 2.1, with f(t) = (t 2 + t + 1) ?1. The second identity derives from Theorem 3.6, for which we have: p 1;2] n;k = (?1) n?k n + k ? 1 2k + 1 : The otherâ€¦ (More)

- Davide Baccherini, Donatella Merlini, Renzo Sprugnoli
- Discrete Mathematics
- 2007

We study the relation between binary words excluding a pattern and proper Riordan arrays. In particular, we prove necessary and sufficient conditions under which the number of words counted withâ€¦ (More)

- Donatella Merlini, Renzo Sprugnoli
- Theor. Comput. Sci.
- 2011

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 everyâ€¦ (More)

- Renza Campagni, Donatella Merlini, M. Cecilia Verri
- CSEDU
- 2014