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)

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)

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)

BACKGROUND
An adequate energy-protein intake (EPI) when combined with amino acid supplementation may have a positive impact on nutritional and metabolic status in patients with chronic heart failureâ€¦ (More)

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)

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)

In this paper we treat the static dictionary problem , very well known in computer science. It consists in storing a set S of m elements in the range [1 . . . n ] so that membership queries on S 'sâ€¦ (More)

In this paper we present the theory of implicit Riordan arrays, that is, Riordan arrays which require the application of the Lagrange Inversion Formula to be dealt with. We show several examples inâ€¦ (More)