The Stanley Depth of Some Power Sets of Multisets
نویسنده
چکیده
In this paper, we study the Stanley depth for the partially ordered set (poset) of nonempty submultisets of a multiset. We find the Stanley depth explicitly for any multiset with at most five distinct elements and provide an upper bound for the general case. On the other hand, the elements of a product of chains corresponds to the submultisets of a multiset. We prove that the Stanley depth of the product of chains n\0 is (n − 1)⌈k2 ⌉. At the end, we show that the Stanley depth for any case of a multiset with n distinct elements can be determined if we know all interval partitions of the poset of nonempty subsets of {1,2,...,n}.
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