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A general framework for island systems

Tutkimustuotosvertaisarvioitu

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A general framework for island systems. / Foldes, S.; Horváth, Eszter K.; Radeleczki, Sándor; Waldhauser, Tamás.

julkaisussa: Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum, Vuosikerta 81, Nro 1-2, 2015, s. 3-24.

Tutkimustuotosvertaisarvioitu

Harvard

Foldes, S, Horváth, EK, Radeleczki, S & Waldhauser, T 2015, 'A general framework for island systems' Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum, Vuosikerta. 81, Nro 1-2, Sivut 3-24. https://doi.org/10.14232/actasm-013-279-7

APA

Foldes, S., Horváth, E. K., Radeleczki, S., & Waldhauser, T. (2015). A general framework for island systems. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum, 81(1-2), 3-24. https://doi.org/10.14232/actasm-013-279-7

Vancouver

Foldes S, Horváth EK, Radeleczki S, Waldhauser T. A general framework for island systems. Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 2015;81(1-2):3-24. https://doi.org/10.14232/actasm-013-279-7

Author

Foldes, S. ; Horváth, Eszter K. ; Radeleczki, Sándor ; Waldhauser, Tamás. / A general framework for island systems. Julkaisussa: Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum. 2015 ; Vuosikerta 81, Nro 1-2. Sivut 3-24.

Bibtex - Lataa

@article{79867c2a35fe406aabf309b7c9899a62,
title = "A general framework for island systems",
abstract = "The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [3]. Results of [3] were starting points for investigations exploring several variations and various aspects of this notion. In this paper we introduce a general framework for islands that subsumes all earlier studied concepts of islands on finite boards, moreover we show that the prime implicants of a Boolean function, the formal concepts of a formal context, convex subgraphs of a simple graph, and some particular subsets of a projective plane also fit into this framework. We axiomatize those cases where islands have the property of being pairwise comparable or disjoint, or they are distant, introducing the notion of a connective island domain and of a proximity domain, respectively. In the general case the maximal systems of islands are characterised by using the concept of an admissible system. We also characterise all possible island systems in the case of connective island domains and proximity domains.",
keywords = "Admissible system, CD-independent and CDW-independent sets, Connected subgraph, Convex subgraph, Distant system, Formal concept, Height function, Island domain, Island system, Point-to-set proximity relation, Prime implicant, Projective plane, Proximity domain",
author = "S. Foldes and Horv{\'a}th, {Eszter K.} and S{\'a}ndor Radeleczki and Tam{\'a}s Waldhauser",
year = "2015",
doi = "10.14232/actasm-013-279-7",
language = "English",
volume = "81",
pages = "3--24",
journal = "Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum",
issn = "0001-6969",
publisher = "University of Szeged",
number = "1-2",

}

RIS (suitable for import to EndNote) - Lataa

TY - JOUR

T1 - A general framework for island systems

AU - Foldes, S.

AU - Horváth, Eszter K.

AU - Radeleczki, Sándor

AU - Waldhauser, Tamás

PY - 2015

Y1 - 2015

N2 - The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [3]. Results of [3] were starting points for investigations exploring several variations and various aspects of this notion. In this paper we introduce a general framework for islands that subsumes all earlier studied concepts of islands on finite boards, moreover we show that the prime implicants of a Boolean function, the formal concepts of a formal context, convex subgraphs of a simple graph, and some particular subsets of a projective plane also fit into this framework. We axiomatize those cases where islands have the property of being pairwise comparable or disjoint, or they are distant, introducing the notion of a connective island domain and of a proximity domain, respectively. In the general case the maximal systems of islands are characterised by using the concept of an admissible system. We also characterise all possible island systems in the case of connective island domains and proximity domains.

AB - The notion of an island defined on a rectangular board is an elementary combinatorial concept that occurred first in [3]. Results of [3] were starting points for investigations exploring several variations and various aspects of this notion. In this paper we introduce a general framework for islands that subsumes all earlier studied concepts of islands on finite boards, moreover we show that the prime implicants of a Boolean function, the formal concepts of a formal context, convex subgraphs of a simple graph, and some particular subsets of a projective plane also fit into this framework. We axiomatize those cases where islands have the property of being pairwise comparable or disjoint, or they are distant, introducing the notion of a connective island domain and of a proximity domain, respectively. In the general case the maximal systems of islands are characterised by using the concept of an admissible system. We also characterise all possible island systems in the case of connective island domains and proximity domains.

KW - Admissible system

KW - CD-independent and CDW-independent sets

KW - Connected subgraph

KW - Convex subgraph

KW - Distant system

KW - Formal concept

KW - Height function

KW - Island domain

KW - Island system

KW - Point-to-set proximity relation

KW - Prime implicant

KW - Projective plane

KW - Proximity domain

UR - http://www.scopus.com/inward/record.url?scp=84938827353&partnerID=8YFLogxK

U2 - 10.14232/actasm-013-279-7

DO - 10.14232/actasm-013-279-7

M3 - Article

VL - 81

SP - 3

EP - 24

JO - Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum

JF - Acta Universitatis Szegediensis: Acta Scientiarum Mathematicarum

SN - 0001-6969

IS - 1-2

ER -