When k ≥ 1 , we say that vectors A and B from Z w are k-crossing if there are coordinates i and j for which A [ i ] − B [ i ] ≥ k and B [ j ] − A [ j ] ≥ k .

May 8, 2012 · This research is motivated by a natural question concerning the width of the lattice of maximum antichains of a partially ordered set.

For positive integers w and k, two vectors A and B from. Zw are called k-crossing if there are two coordinates i and j.

What is the maximum size of a family of pairwise $1$-crossing and pairwise non-$k$-crossing vectors in $\mathbb{Z}^w$? We state a conjecture that the answer is ...

For positive integers w and k, two vectors A and B from Z(w) are called k-crossing if there are two coordinates i and j such that A[i] - B[i] >= k and B[j] ...

F family of pairwise incomparable non-k-crossing vectors in Z3 minimizing max{|a3 − b3| : a,b ∈ F} levels: Fi = {a ∈ F : a3 = i} con ict digraph on F:.

Abstract. For positive integers w and k, two vectors A and B from Z^w are called k-crossing if there are two coordinates i and j such that A[i]-B[i]>=k and B[j]- ...

This paper shows that when k and w are positive integers, there exists an integer t = t(k,w) and an on-line algorithm that will construct an on theline ...

For positive integers w and k, two vectors A and B from Z w are called k-crossing if there are two coordinates i and j such that A i - B i k and B j - A j k ...

Extremal Problem for Crossing Vectors. Vectors v and u in the lattice Zw i-cross if there exists a coordinate on which v is i bigger then u and vice versa.