Add to ORKGAn (n)completely separating system C ((n)CSS) is a collection of blocks of [n] = {1,...,n} such that for all distinct a, b Є C with a Є A B and b Є B A. An (n)CSS is minimal if it contains the minimum possible number of blocks for a CSS on [n]. The number of non-isomorphic minimal (n)CSSs is determined for 11 ≤ n ≤ 35. This also provides an enumeration of a natural class of antichains
A subset $A$ of $\mathbb{Z}^n$ is called a weak antichain if it does not contain two elements $x$ an...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, …, n} o...
AbstractLet H be a finite set, and A1, A2, …, Am subsets of H. We call a system A separating system,...
This paper extends known results on the existence, number and structure of antichains and completely...
AbstractLet M be a finite set consisting of ki elements of type i, i = 1, 2,…, n and let S denote th...
R(n) denotes the minimum possible size of a completely separating system C on an n-set. R(n, h, k) d...
Let n ⩾4 be a natural number, and let K be a set K⊆[n]:={1,2,...,n}. We study the problem of finding...
AbstractLet f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n ...
AbstractWe consider coverings of the Boolean n-cube Bn={0,1}n by families of its subsets of the spec...
AbstractIn this paper we define a completely separating system of an n-set, an extension of the conc...
AbstractA set F of distinct subsets x of a finite multiset M (that is, a set with several different ...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1,…,n} ord...
Let n> 3 be a natural number. We study the problem to find the smallest r such that there is a fa...
AbstractA short proof of the following result of Kleitman is given: the total number of sets contain...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
A subset $A$ of $\mathbb{Z}^n$ is called a weak antichain if it does not contain two elements $x$ an...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, …, n} o...
AbstractLet H be a finite set, and A1, A2, …, Am subsets of H. We call a system A separating system,...
This paper extends known results on the existence, number and structure of antichains and completely...
AbstractLet M be a finite set consisting of ki elements of type i, i = 1, 2,…, n and let S denote th...
R(n) denotes the minimum possible size of a completely separating system C on an n-set. R(n, h, k) d...
Let n ⩾4 be a natural number, and let K be a set K⊆[n]:={1,2,...,n}. We study the problem of finding...
AbstractLet f(n) be the smallest integer t such that a poset obtained from a Boolean lattice with n ...
AbstractWe consider coverings of the Boolean n-cube Bn={0,1}n by families of its subsets of the spec...
AbstractIn this paper we define a completely separating system of an n-set, an extension of the conc...
AbstractA set F of distinct subsets x of a finite multiset M (that is, a set with several different ...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1,…,n} ord...
Let n> 3 be a natural number. We study the problem to find the smallest r such that there is a fa...
AbstractA short proof of the following result of Kleitman is given: the total number of sets contain...
AbstractLet 2n_ be the ordered set obtained from the Boolean lattice 2n by deleting both the greates...
A subset $A$ of $\mathbb{Z}^n$ is called a weak antichain if it does not contain two elements $x$ an...
AbstractLet 2[n] denote the Boolean lattice of order n, that is, the poset of subsets of {1, …, n} o...
AbstractLet H be a finite set, and A1, A2, …, Am subsets of H. We call a system A separating system,...