Abstract The paper gives characterizations of the supernorm statistic $$\widehat{N} :\mathcal {P}\rightarrow \mathbb {N}^{+}$$ N ^ : P → + for partitions,...

We define Dumont’s statistic on the symmetric group Sn to be the function dmc: Sn → N which maps a permutation σ to the number of distinct nonzero letters in code(σ). Dumont showed that this statistic is Eulerian. Naturally extending Dumont’s statistic to the rearrangement classes of arbitrary words, we create a generalized statistic which is again Eulerian. As a consequence, we show that for e...

Sample covariance matrices are also of essential importance in multivariate statistical analysis because many test statistics involve their eigenvalues and/or eigenvectors. The typical example is T 2 statistic, which was proposed by Hotelling [2]. We refer to [1] and [3] for various uses of the T 2 statistic. The T 2 statistic, which is the origin of multivariate linear hypothesis tests and the...