2 research outputs found
Interval-Dismantling for Lattices
Dismantling allows for the removal of elements of a set, or in our case
lattice, without disturbing the remaining structure. In this paper we have
extended the notion of dismantling by single elements to the dismantling by
intervals in a lattice. We utilize theory from Formal Concept Analysis (FCA) to
show that lattices dismantled by intervals correspond to closed subrelations in
the respective formal context, and that there exists a unique kernel with
respect to dismantling by intervals. Furthermore, we show that dismantling
intervals can be identified directly in the formal context utilizing a
characterization via arrow relations and provide an algorithm to compute all
dismantling intervals.Comment: 12 pages, 5 figures, 1 algorith