Let Xi,X2,... ,Xk be k disjoint subsets of S with the same cardinality m. Define H（m,k） = {X lahtain in S ： X ￠Xi for 1 ≤ i≤ k} and P（m,k） = {X lohtain ni S ： X ∩ Xi ≠0 for at least two Xi＇s}. Suppose S=U...Let Xi,X2,... ,Xk be k disjoint subsets of S with the same cardinality m. Define H（m,k） = {X lahtain in S ： X ￠Xi for 1 ≤ i≤ k} and P（m,k） = {X lohtain ni S ： X ∩ Xi ≠0 for at least two Xi＇s}. Suppose S=Ui=1^k Xi , and let Q（m, k, 2） be the collection of all subsets K of S satisfying ｜K ∩ Xi｜ ≥ 2 for some 1 ≤ i ≤ k. For any two disjoint subsets Yi and Y2 of S, we define F1,j = {X lahtain in S ： either ｜X ∩Y1｜≥1 or ｜X ∩ Y2｜≥ j}. It is obvious that the four posets are graded posets ordered by inclusion. In this paper we will prove that the four posets are nested chain orders.展开更多
基金the National Natural Science Foundation of China （No. 10471016）.
文摘Let Xi,X2,... ,Xk be k disjoint subsets of S with the same cardinality m. Define H（m,k） = {X lahtain in S ： X ￠Xi for 1 ≤ i≤ k} and P（m,k） = {X lohtain ni S ： X ∩ Xi ≠0 for at least two Xi＇s}. Suppose S=Ui=1^k Xi , and let Q（m, k, 2） be the collection of all subsets K of S satisfying ｜K ∩ Xi｜ ≥ 2 for some 1 ≤ i ≤ k. For any two disjoint subsets Yi and Y2 of S, we define F1,j = {X lahtain in S ： either ｜X ∩Y1｜≥1 or ｜X ∩ Y2｜≥ j}. It is obvious that the four posets are graded posets ordered by inclusion. In this paper we will prove that the four posets are nested chain orders.
