We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG (n; 2) ordered by inclusion. For given k; ` (k < `) and m the problem is to nd a family of size m in the set of`-subspaces of PG (n; 2), containing the minimal number of k-subspaces. We introduce two lexicographic type orders O 1 and O 2 on the set of`-subspaces, and prove that the rst m of them, take...

Statistical tests are powerful tools for data analysis. Kruskal-Wallis test is a non-parametric statistical test that evaluates whether two or more samples are drawn from the same distribution. It is commonly used in various areas. But sometimes, the use of the method is impeded by privacy issues raised in fields such as biomedical research and clinical data analysis because of the confidential...