Nonexistence of a Kruskal-Katona Type Theorem for Subword Orders
نویسنده
چکیده
We consider the poset SO(n) of all words over an n{element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i.e. there is a theorem of Kruskal{Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip{order can be chosen. Daykin introduced the V {order which generalizes the vip{order to the n 2 case. He conjectured that the V {order gives a Kruskal{Katona type theorem for SO(n). We show that this conjecture fails for all n 3 by explicitely giving a counterexample. Based on this, we prove that for no n 3 the subword order SO(n) is a Macaulay poset.
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عنوان ژورنال:
- Combinatorica
دوره 24 شماره
صفحات -
تاریخ انتشار 2004