On the vector space of 0-configurations |
| |
Authors: | M Deza P Frankl |
| |
Institution: | (1) C.N.R.S., 54 Bd. Raspail, 75006 Paris, France |
| |
Abstract: | Let α be a rational-valued set-function on then-element sexX i.e. α(B) εQ for everyB ⫅X. We say that α defines a 0-configuration with respect toA⫅2
x
if for everyA εA we have
α(B)=0. The 0-configurations form a vector space of dimension 2
n
− |A| (Theorem 1). Let 0 ≦t<k ≦n and letA={A ⫅X: |A| ≦t}. We show that in this case the 0-configurations satisfying α(B)=0 for |B|>k form a vector space of dimension
, we exhibit a basis for this space (Theorem 4). Also a result of Frankl, Wilson 3] is strengthened (Theorem 6). |
| |
Keywords: | 05 C 65 05 C 35 15 A 03 |
本文献已被 SpringerLink 等数据库收录! |
|