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- W1504909829 abstract "We define and study a new depth, related to the Stanley depth, for the partially ordered set (poset) of nonempty submultisets of a multiset. We find the new 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 new depth of the product of chains $bm{n}^kbackslash bm{0}$ is $(n-1)lceil{kover 2}rceil$. We also show that the new 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,...,$n$}." @default.
- W1504909829 created "2016-06-24" @default.
- W1504909829 creator A5077958968 @default.
- W1504909829 date "2009-08-25" @default.
- W1504909829 modified "2023-09-27" @default.
- W1504909829 title "A New Depth Related to the Stanley Depth of Some Power Sets of Multisets" @default.
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- W1504909829 hasPublicationYear "2009" @default.
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