By “straightforward” we mean that it can be presented in a standard one-variable calculus course. This is not the first time an “elementary” proof of this identity has been given. Several other proofs can be found in, e.g., [1], [3], [4], [5], [7]. Most of them are variations on a theme (double integral, gamma function, . . . ). This one is a simplification of one of the most recent ones by Lor...

for some N ≥ k + 1, then the equality in (1.2) occurs only when a = 0. Kruskal-Macaulay functions are relevant for their applications to the study of antichains in multisets (see for example [11, 2]), posets, rings and polyhedral combinatorics (see [5] and the survey [3]). In particular, they play and important role in proving results, extensions and generalizations of classical problems concer...

The present note generalizes Wallis’ formula, 2  =  . 7 6 . 5 6 . 5 4 . 3 4 . 3 2 . 1 2 , using the EulerMascheroni constant g and the Glaisher-Kinkelin constant A: 2 ln 2 4 = 3 3 2 . 1 2 . 5 4 3 4

A Steiner star for a set P of n points in R connects an arbitrary center point to all points of P , while a star connects a point p ∈ P to the remaining n−1 points of P . All connections are realized by straight line segments. Fekete and Meijer showed that the minimum star is at most √ 2 times longer than the minimum Steiner star for any finite point configuration in R. The maximum ratio betwee...

In a multi-group experimental design where interest is in a univariate response, the nonparametric Kruskal-Wallis test [Kniskal and Wallis (1952)] provides a potentially more powerful alternative to the parametric one-way analysis of variance when the assumptions of normality are in question. For multivariate response, Puri and Sen (1966) proposed a generalization of the KmskalWallis test that ...