%0 Generic %1 felde2022intervaldismantling %A Felde, Maximilian %A Koyda, Maren %D 2022 %K %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 = {2023-12-13T06:09:03.000+0100}, author = {Felde, Maximilian and Koyda, Maren}, biburl = {https://www.bibsonomy.org/bibtex/23cd2993bfff6d11a7c48d4b57895b953/admin}, doi = {10.48550/arXiv.2208.01479}, interhash = {aaf214fd2dbc179af674360061ad41d8}, intrahash = {3cd2993bfff6d11a7c48d4b57895b953}, keywords = {}, note = {cite arxiv:2208.01479Comment: 12 pages, 5 figures, 1 algorithm}, timestamp = {2023-12-13T06:09:03.000+0100}, title = {Interval-Dismantling for Lattices}, url = {https://arxiv.org/abs/2208.01479}, year = 2022 }