We present an analog of the well-known Kruskal-Katona theorem for the poset of subspaces of PG (n; 2) ordered by inclusion. For given k; ` (k ! `) and m the problem is to find a family of size m in the set of `-subspaces of PG (n; 2), containing the minimal number of k-subspaces. We introduce two lexicographic type orders O 1 and O 2 on the set of `-subspaces, and prove that the first m of them, taken in the order O 1 , provide a solution in the case k = 0 and arbitrary ` ? 0, and one taken in the order O 2 , provide a solution in the case ` = n \Gamma 1 and arbitrary k ! n \Gamma 1. Concerning other values of k and `, we show that for n 3 the considered poset is not Macaulay by constructing a counterexample in the case ` = 2 and k...
AbstractFor an n-tuple t = (t1,t2,…,tn) of integers satisfying 1⩽t1⩽t2···⩽tn, T(t)=T denotes the ran...
AbstractTo each k-dimensional subspace of an n-dimensional vector space ove GF(q) we assign a number...
The focus of this work is studying f-vectors in a relative setting. The Kruskal-Katona theorem is a ...
We present an analog of the well-known Kruskal–Katona theorem for the poset of subspaces of PG(n,2) ...
AbstractWe present an analog of the well-known Kruskal–Katona theorem for the poset of subspaces of ...
Macaulay posets are posets for which there is an analogue of the classical Kruskal-Katona theorem fo...
Macaulay posets are posets for which there is an analogue of the classical Kruskal-Katona theorem fo...
Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a ...
We show for k = 2 that if q = 3 and n = 2k + 1, or q = 2 and n = 2k + 2, then any intersecting famil...
AbstractLet [m]n denote the set of all n-tuples of the integers {0, 1, …, m − 1}, partially ordered ...
AbstractThe main result of this article is in proving a conjecture by Sali. We obtain a Kruskal–Kato...
We classify the smallest two fold blocking sets with respect to the (n-k)-spaces in PG(n, 2).We show...
AbstractWe give a very short proof for the Kruskal-Katona theorem and Lovász's version of it: given ...
The boolean hierarchy of k-partitions over NP for k >= 3 was introduced as a generalization of th...
Given a finite poset P, the intensively studied quantity La(n, P) denotes the largest size of a fami...
AbstractFor an n-tuple t = (t1,t2,…,tn) of integers satisfying 1⩽t1⩽t2···⩽tn, T(t)=T denotes the ran...
AbstractTo each k-dimensional subspace of an n-dimensional vector space ove GF(q) we assign a number...
The focus of this work is studying f-vectors in a relative setting. The Kruskal-Katona theorem is a ...
We present an analog of the well-known Kruskal–Katona theorem for the poset of subspaces of PG(n,2) ...
AbstractWe present an analog of the well-known Kruskal–Katona theorem for the poset of subspaces of ...
Macaulay posets are posets for which there is an analogue of the classical Kruskal-Katona theorem fo...
Macaulay posets are posets for which there is an analogue of the classical Kruskal-Katona theorem fo...
Extending a classical theorem of Sperner, we characterize the integers $m$ such that there exists a ...
We show for k = 2 that if q = 3 and n = 2k + 1, or q = 2 and n = 2k + 2, then any intersecting famil...
AbstractLet [m]n denote the set of all n-tuples of the integers {0, 1, …, m − 1}, partially ordered ...
AbstractThe main result of this article is in proving a conjecture by Sali. We obtain a Kruskal–Kato...
We classify the smallest two fold blocking sets with respect to the (n-k)-spaces in PG(n, 2).We show...
AbstractWe give a very short proof for the Kruskal-Katona theorem and Lovász's version of it: given ...
The boolean hierarchy of k-partitions over NP for k >= 3 was introduced as a generalization of th...
Given a finite poset P, the intensively studied quantity La(n, P) denotes the largest size of a fami...
AbstractFor an n-tuple t = (t1,t2,…,tn) of integers satisfying 1⩽t1⩽t2···⩽tn, T(t)=T denotes the ran...
AbstractTo each k-dimensional subspace of an n-dimensional vector space ove GF(q) we assign a number...
The focus of this work is studying f-vectors in a relative setting. The Kruskal-Katona theorem is a ...
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