In this note we consider unimodality problems of sequences of multinomial coefficients and symmetric functions. The results presented here generalize our early results for binomial coefficients. We also give an answer to a question of Sagan about strong q-log-concavity of certain sequences of symmetric functions, which can unify many known results for q-binomial coefficients and q-Stirling numb...

For several pairs (P,Q) of classical distributions on N0, we show that their stochastic ordering P ≤st Q can be characterized by their extreme tail ordering equivalent to P ({k∗})/Q({k∗}) ≤ 1 ≤ limk→k∗ P ({k})/Q({k}), with k∗ and k∗ denoting the minimum and the supremum of the support of P + Q, and with the limit to be read as P ({k∗})/Q({k∗}) for k∗ finite. This includes in particular all pair...

Abstract In this note, we estimate the distance between two q -nomial coefficients ( k n ) q - ? {\left( {_k^n} \right)_q} - {_{k'}^...

Sums of the form $\sum_{q \leq N_1 < \cdots N_m n}{a_{(m);N_m}\cdots a_{(2);N_2}a_{(1);N_1}}$ date back to sixteen century when Vi\`ete illustrated that relation linking roots and coefficients a polynomial had this form. In more recent years, such sums have become increasingly used with diversity applications. paper, we develop formulae help manipulating (which will refer as multiple sums). We ...