Let m, n, S_1, S_2, …, S_n, be non-negative integers with 0≤m≤n. Assume μ(S_1, S_2, …, S_n)={(a_1, a_2, …, a_n)|0≤a_i≤S_i for each i} is a poser, Where (a_1, a_2, …, a_n)<(b_1, b_2, …, b_n) if and only if...Let m, n, S_1, S_2, …, S_n, be non-negative integers with 0≤m≤n. Assume μ(S_1, S_2, …, S_n)={(a_1, a_2, …, a_n)|0≤a_i≤S_i for each i} is a poser, Where (a_1, a_2, …, a_n)<(b_1, b_2, …, b_n) if and only if a_i<b_i for all i. A subset of μ(s_1, s_2, …, S_n) is called a two-part Sperner family in μ(s_1, s_2, …, s_n) if for any a=(a_1, a_2, …, an), b=(b_1, b_2, …, b_n) ∈μ(s_1, s_2, …, s_n), (i) a_i=b_i(1≤i≤m) and a_i≤b_i(m+1≤i≤n) imply a_i=b_i for all i, and (ⅱ) a_i≤b_i(1≤i≤m) and a_i=b_i(m+1≤i≤n) imply a_i=b_i for all i.In this paper, we prove that if is a two-part Sperner family in μ(s_1, s_2,…, s_n), then展开更多
文摘Let m, n, S_1, S_2, …, S_n, be non-negative integers with 0≤m≤n. Assume μ(S_1, S_2, …, S_n)={(a_1, a_2, …, a_n)|0≤a_i≤S_i for each i} is a poser, Where (a_1, a_2, …, a_n)<(b_1, b_2, …, b_n) if and only if a_i<b_i for all i. A subset of μ(s_1, s_2, …, S_n) is called a two-part Sperner family in μ(s_1, s_2, …, s_n) if for any a=(a_1, a_2, …, an), b=(b_1, b_2, …, b_n) ∈μ(s_1, s_2, …, s_n), (i) a_i=b_i(1≤i≤m) and a_i≤b_i(m+1≤i≤n) imply a_i=b_i for all i, and (ⅱ) a_i≤b_i(1≤i≤m) and a_i=b_i(m+1≤i≤n) imply a_i=b_i for all i.In this paper, we prove that if is a two-part Sperner family in μ(s_1, s_2,…, s_n), then
