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.
%0 Generic
%1 felde2022intervaldismantling
%A Felde, Maximilian
%A Koyda, Maren
%D 2022
%K myown
%R 10.48550/arXiv.2208.01479
%T Interval-Dismantling for Lattices
%U https://arxiv.org/abs/2208.01479
%X 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.
@preprint{felde2022intervaldismantling,
abstract = {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.},
added-at = {2023-12-12T12:49:02.000+0100},
author = {Felde, Maximilian and Koyda, Maren},
biburl = {https://www.bibsonomy.org/bibtex/23cd2993bfff6d11a7c48d4b57895b953/kde-alumni},
doi = {10.48550/arXiv.2208.01479},
interhash = {aaf214fd2dbc179af674360061ad41d8},
intrahash = {3cd2993bfff6d11a7c48d4b57895b953},
keywords = {myown},
note = {cite arxiv:2208.01479Comment: 12 pages, 5 figures, 1 algorithm},
timestamp = {2023-12-12T12:49:02.000+0100},
title = {Interval-Dismantling for Lattices},
url = {https://arxiv.org/abs/2208.01479},
year = 2022
}