Year: 2026
Type: article
Abstract: Let R be an axis-aligned rectangle. We define a floorplan as a partition of R into rectangular regions (rooms) such that each vertex is shared by at most three rooms. Following the approach of Nakano et al.,we also assume the presence of a set of points that impose constraints on the walls passing through them, allowing only horizontal or vertical segments. These constraints can be encoded by a permutation matrix whose entries are labeled H and V, which we refer to as a pattern matrix. In this work, we characterize the well-known classes of guillotine, diagonal, and diagonal–guillotine floorplans in terms of the presence of specific families of pattern matrices. In this way, we translate a purely geometric characterization into a combinatorial one.
Source: Mathematics
DOI: 10.3390/math14020310
Authors: Andrea Frosini, Elisa Pergola, Simone Rinaldi
Institutions: University of Florence, University of Siena
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
Award: G5636153502
OpenAlex ID: W7124303141
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