A new approach to Macaulay posets
نویسندگان
چکیده
We develop a new approach for establishing the Macaulayness of posets representable as cartesian powers of other posets. This approach is based on a problem of constructing an ideal of maximum rank in a poset. Using the relations between the maximum rank ideal problem and the edge-isoperimetric problem on graphs we demonstrate an application of our approach to specification of all posets with a special Macaulay order. We also present a new general construction for additive Macaulay posets and introduce several new families of Macaulay posets.
منابع مشابه
Some New Results on Macaulay Posets
Macaulay posets are posets for which there is an analogue of the classical KruskalKatona theorem for finite sets. These posets are of great importance in many branches of combinatorics and have numerous applications. We survey mostly new and also some old results on Macaulay posets. Emphasis is also put on construction of extremal ideals in Macaulay posets.
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ورودعنوان ژورنال:
- J. Comb. Theory, Ser. A
دوره 105 شماره
صفحات -
تاریخ انتشار 2004