Linear Inequalities for Flags in Graded Partially Ordered Sets
نویسندگان
چکیده
منابع مشابه
Linear Inequalities for Flags in Graded Posets
The closure of the convex cone generated by all flag f -vectors of graded posets is shown to be polyhedral. In particular, we give the facet inequalities to the polar cone of all nonnegative chain-enumeration functionals on this class of posets. These are in one-to-one correspondence with antichains of intervals on the set of ranks and thus are counted by Catalan numbers. Furthermore, we prove ...
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We characterize the linear inequalities satisfied by flag f -vectors of all finite bounded posets. We do the same for semipure posets. In particular, the closed convex cone generated by flag f -vectors of bounded posets of fixed rank is shown to be simplicial, and the closed cone generated by flag f -vectors of semipure posets of fixed rank is shown to be polyhedral. The extreme rays of both of...
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In this paper, we introduce tripled partially ordered sets and monotone functions on tripled partiallyordered sets. Some basic properties on these new dened sets are studied and some examples forclarifying are given.
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The linear discrepancy of a poset P is the least k for which there is a linear extension L of P such that if x and y are incomparable in P, then |hL(x) − hL(y)| ≤ k, where hL(x) is the height of x in L. In this paper, we consider linear discrepancy in an online setting and devise an online algorithm that constructs a linear extension L of a poset P so that |hL(x) − hL(y)| ≤ 3k − 1, when the lin...
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To my parents, Jim and Karol, who believed a farm kid from North Dakota could do whatever he wanted and helped me achieve whatever I imagined and more. iii ACKNOWLEDGEMENTS There are many people without whose mentoring, guidance, support, and friendship this dissertation never would have been written. My advisor, William T. Trotter, is at the top of that list. I have greatly enjoyed working wit...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.1999.3008