منابع مشابه
A Kruskal - Katona Type Theorem for the
We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG (n; 2) ordered by inclusion. For given k; ` (k < `) and m the problem is to nd a family of size m in the set of`-subspaces of PG (n; 2), containing the minimal number of k-subspaces. We introduce two lexicographic type orders O 1 and O 2 on the set of`-subspaces, and prove that the rst m of them, take...
متن کاملShifting shadows: the Kruskal–Katona Theorem
As we have seen, antichains and intersecting families are fundamental to Extremal Set Theory. The two central theorems, Sperner’s Theorem and the Erdős–Ko–Rado Theorem, have inspired decades of research since their discovery, helping establish Extremal Set Theory as a vibrant and rapidly growing area of Discrete Mathematics. One must, then, pay a greater than usual amount of respect to the Krus...
متن کاملApproximations to the Kruskal-katona Theorem
Approximations to the Kruskal-Katona theorem are stated and proven. These approximations are weaker than the theorem, but much easier to work with numerically.
متن کاملA Kruskal-Katona type theorem for graphs
A bound on consecutive clique numbers of graphs is established. This bound is evaluated and shown to often be much better than the bound of the Kruskal-Katona theorem. A bound on non-consecutive clique numbers is also proven.
متن کاملOn Γ-vectors Satisfying Kruskal-katona Inequalities
We present examples of flag homology spheres whose γvectors satisfy the Kruskal-Katona inequalities. This includes several families of well-studied simplicial complexes, including Coxeter complexes and the simplicial complexes dual to the associahedron and to the cyclohedron. In another direction, we show that if a flag (d− 1)-sphere has at most 2d + 2 vertices its γ-vector satisfies the Kruska...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 1976
ISSN: 0097-3165
DOI: 10.1016/0097-3165(76)90069-8