An Erdős-Ko-Rado theorem for multisets (Q5903815)

Given integers \(k_ n\leq...\leq k_ 1\), the multiset \(M(k_ n,...,k_ 1)\) consists of the all vectors \(\vec x=(x_ n,...,x_ 1)\), where the \(x_ i\) are integers satisfying \(0\leq x_ i\leq k_ i\). The author gives two proofs of a refinement of Erdős-Ko-Rado Theorem stated by \textit{C. Greene} and \textit{D. J. Kleitman} [M.A.A. Stud. Math., Vol. 17, Studies in Combinatorics (1978; Zbl 0409.05012)]. \{The author shows by means of an example that the proof technique of Greene and Kleitman appears to be not quite correct.\}