One of the main features of crystallization theory relies on the purely combinatorial nature of the representing objects, which makes them particularly suitable for computer manipulation. This fact allows a computational approach to the study of PL n-manifolds, which has been performed by means of several functions, collected in a unified program, called DUKE III. DUKE III allows automatic manipulation of edge-coloured graphs representing PL n-manifolds (code computation, checking possible isomorphism between edge-coloured graphs, construction of boundary graph, checking bipartition, connectedness, rigidity and planarity conditions, combinatorial moves, invariants computation...). Furthermore, DUKE III allows automatic recognition of orientable 3-manifolds triangulated by at most 30 coloured tetrahedra and of non-orientable 3-manifolds triangulated by at most 26 coloured tetrahedra (by making use of existing electronic archives of all rigid bipartite crystallizations up to 30 vertices and non-bipartite ones up to 26 vertices, due to the same research team).

DUKE III: A program to handle edge-coloured graphs representing PL n-dimensional manifolds / Casali, Maria Rita; Cristofori, Paola. - ELETTRONICO. - (2007).

DUKE III: A program to handle edge-coloured graphs representing PL n-dimensional manifolds

CASALI, Maria Rita;CRISTOFORI, Paola
2007

Abstract

One of the main features of crystallization theory relies on the purely combinatorial nature of the representing objects, which makes them particularly suitable for computer manipulation. This fact allows a computational approach to the study of PL n-manifolds, which has been performed by means of several functions, collected in a unified program, called DUKE III. DUKE III allows automatic manipulation of edge-coloured graphs representing PL n-manifolds (code computation, checking possible isomorphism between edge-coloured graphs, construction of boundary graph, checking bipartition, connectedness, rigidity and planarity conditions, combinatorial moves, invariants computation...). Furthermore, DUKE III allows automatic recognition of orientable 3-manifolds triangulated by at most 30 coloured tetrahedra and of non-orientable 3-manifolds triangulated by at most 26 coloured tetrahedra (by making use of existing electronic archives of all rigid bipartite crystallizations up to 30 vertices and non-bipartite ones up to 26 vertices, due to the same research team).
2007
Casali, Maria Rita; Cristofori, Paola
File in questo prodotto:
Non ci sono file associati a questo prodotto.
Pubblicazioni consigliate

Licenza Creative Commons
I metadati presenti in IRIS UNIMORE sono rilasciati con licenza Creative Commons CC0 1.0 Universal, mentre i file delle pubblicazioni sono rilasciati con licenza Attribuzione 4.0 Internazionale (CC BY 4.0), salvo diversa indicazione.
In caso di violazione di copyright, contattare Supporto Iris

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/594080
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? ND
social impact