论文部分内容阅读
A restricted signed r-set is a pair(A,f),where A■[n]={1,2,…,n} is an r-set and f is a map from A to[n]with f(i)≠i for all i∈A.For two restricted signed sets(A,f) and(B,g),we define an order as (A,f)≤(B,g) if A■ B and g|A=f.A family A of restricted signed sets on[n]is an intersecting antichain if for any(A,f),(B,g)∈A,they are incomparable and there exists x∈A∩B such that f(x)=g(x).In this paper,we first give a LYM-type inequality for any intersecting antichain A of restricted signed sets,from which we then obtain |A|≤■(n-1)~(r-1) if A consists of restricted signed r-sets on[n].Unless r=n=3,equality holds if and only if A consists of all restricted signed r-sets(A,f) such that x_0∈A and f(x_0)=ε_0 for some fixed x_0∈[n],ε_0∈[n]{x_0}.
A restricted signed r-set is a pair (A, f), where A ■ [n] = {1,2, ..., n} is an r-set and f is a map from A to [n] with f i) ≠ i for all i∈A.For two restricted signed sets (A, f) and (B, g), we define an order as (A, f) ≤ (B, g) if A ■ B and g | A = fA family A of restricted signed sets on [n] is an intersecting antichain if for any (A, f), (B, g) ∈A, they are incomparable and there exists x∈A∩B such that f (x ) = g (x) .In this paper, we first give a LYM-type inequality for any intersecting antichain A of restricted signed sets, from which we then obtain | A | ≦ ■ (n-1) to (r- 1) if A consists of restricted signed r-sets on [n] .Unless r = n = 3, equality holds if and only if A consists of all restricted signed r-sets (A, f) such that x_0∈A and f (x_0 ) = ε_0 for some fixed x_0∈ [n], ε_0∈ [n] {x_0}.