We present a class of strongly q-log-convex polynomials based on a triangular recurrence relation with linear coefficients, and we show that the Bell polynomials, the Bessel polynomials, theâ€¦ (More)

We prove a conjecture of Liu and Wang on the q-log-convexity of the Narayana polynomials of type B. By using Pieriâ€™s rule and the JacobiTrudi identity for Schur functions, we obtain an expansion of aâ€¦ (More)

We prove two recent conjectures of Liu and Wang by establishing the strong q-log-convexity of the Narayana polynomials, and showing that the Narayana transformation preserves log-convexity. We beginâ€¦ (More)

We show that the limiting distributions of the coefficients of the qCatalan numbers and the generalized q-Catalan numbers are normal. Despite the fact that these coefficients are not unimodal forâ€¦ (More)

A family of k-subsets A1, A2, . . . , Ad on [n] = {1, 2, . . . , n} is called a (d, c)-cluster if the union A1 âˆª A2 âˆª Â· Â· Â· âˆª Ad contains at most ck elements with c < d. Let F be a family ofâ€¦ (More)

A 2-coloring of the n-cube in the n-dimensional Euclidean space can be considered as an assignment of weights of 1 or 0 to the vertices. Such a colored ncube is said to be balanced if its center ofâ€¦ (More)

We prove a conjecture of Liu and Wang on the q-log-convexity of the polynomial sequence { âˆ‘n k=0 ( n k )2 q}nâ‰¥0. By using Pieriâ€™s rule and the Jacobi-Trudi identity for Schur functions, we obtain anâ€¦ (More)

Let p(n) denote the partition function. DeSalvo and Pak proved that p(nâˆ’1) p(n) ( 1 + 1 n ) > p(n) p(n+1) for n â‰¥ 2. Moreover, they conjectured that a sharper inequality p(nâˆ’1) p(n) ( 1 + Ï€ âˆš 24n3/2â€¦ (More)

Let L = {Î»1, . . . , Î»s} be a set of s non-negative integers with Î»1 < Î»2 < Â· Â· Â· < Î»s, and let t â‰¥ 2. A family F of subsets of an n-element set is called t-wise L-intersecting if the cardinality ofâ€¦ (More)