منابع مشابه
A new approach to Macaulay posets
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...
متن کاملOptimal antichains and ideals in Macaulay posets
A ranked poset P is a Macaulay poset if there exists a linear ordering of its elements such that for any i and any subset F of the i{th level N i the shadow of the jFj smallest elements of N i w.r.t. is contained in the set of the smallest j(F)j elements of N i?1 , where (F) denotes the shadow of F. We consider the following three optimization problems for P : (i) Find the maximum weight of an ...
متن کاملOn Sequentially Cohen-macaulay Complexes and Posets
The classes of sequentially Cohen-Macaulay and sequentially homotopy Cohen-Macaulay complexes and posets are studied. First, some different versions of the definitions are discussed and the homotopy type is determined. Second, it is shown how various constructions, such as join, product and rank-selection preserve these properties. Third, a characterization of sequential Cohen-Macaulayness for ...
متن کاملSome 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.
متن کاملOn Posets whose Products are Macaulay
If P is an upper semilattice whose Hasse diagram is a tree and whose cartesian powers are Macaulay, it is shown that Hasse diagram of P is actually a spider in which all the legs have the same length.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2005
ISSN: 1077-8926
DOI: 10.37236/33