A Kruskal-Katona type theorem for the linear lattice

被引:3
作者
Bezrukov, S
Blokhuis, A
机构
[1] Univ Paderborn, Dept Math & Comp Sci, D-33101 Paderborn, Germany
[2] Eindhoven Univ Technol, Dept Math & Comp Sci, NL-5600 MB Eindhoven, Netherlands
关键词
D O I
10.1006/eujc.1998.0274
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We present an analog of the well-known Kruskal-Katona theorem For the poser of subspaces of PG(n, 2) ordered by inclusion. For given k, l (k < l) and in the problem is to find a family of size in in the set of l-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 l-subspaces, and prove that the first m of them, taken in the order O-1, provide a solution in the case k = 0 and arbitrary l > 0, and one taken in the order O-2, provide a solution in the case l = n - 1 and arbitrary k < n - 1. Concerning other values of k and l, we show that for n greater than or equal to 3 the considered poser is not Macaulay by constructing a counterexample in the case l = 2 and k = 1. (C) 1999 Academic Press.
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页码:123 / 130
页数:8
相关论文
共 3 条
[1]  
[Anonymous], 1997, ENCY MATH ITS APPL
[2]  
Katona G.O.H., 1968, THEORY GRAPHS, P187
[3]  
Kruskal, 1963, MATH OPTIMIZATION TE, P251