scholarly journals Telescopic groups and symmetries of combinatorial maps

2020 ◽  
Vol 3 (2) ◽  
pp. 483-508
Author(s):  
Rémi Bottinelli ◽  
Laura Grave de Peralta ◽  
Alexander Kolpakov
Keyword(s):  
Combinatorial Maps

scholarly journals Compact combinatorial maps: A volume mesh data structure

2013 ◽  
Vol 75 (3) ◽  
pp. 149-156 ◽  
Author(s):  
Xin Feng ◽  
Yuanzhen Wang ◽  
Yanlin Weng ◽  
Yiying Tong
Keyword(s):  
Data Structure ◽  
Combinatorial Maps ◽  
Volume Mesh

scholarly journals Functional specification and prototyping with oriented combinatorial maps

2000 ◽  
Vol 16 (2) ◽  
pp. 129-156 ◽  
Author(s):  
Jean-François Dufourd ◽  
François Puitg
Keyword(s):  
Functional Specification ◽  
Combinatorial Maps

An error-tolerant approximate matching algorithm for labeled combinatorial maps

2015 ◽  
Vol 156 ◽  
pp. 211-220 ◽  
Author(s):  
Tao Wang ◽  
Hua Yang ◽  
Congyan Lang ◽  
Songhe Feng
Keyword(s):  
Matching Algorithm ◽  
Approximate Matching ◽  
Combinatorial Maps

scholarly journals Connected Chord Diagrams and Bridgeless Maps

10.37236/7400 ◽  
2019 ◽  
Vol 26 (4) ◽  
Author(s):  
Julien Courtiel ◽  
Karen Yeats ◽  
Noam Zeilberger
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lambda Calculus ◽  
The Other ◽  
Combinatorial Proof ◽  
Quantum Field ◽  
Technical Parameter ◽  
Simple Application ◽  
Chord Diagrams ◽  
Combinatorial Maps

We present a surprisingly new connection between two well-studied combinatorial classes: rooted connected chord diagrams on one hand, and rooted bridgeless combinatorial maps on the other hand. We describe a bijection between these two classes, which naturally extends to indecomposable diagrams and general rooted maps. As an application, this bijection provides a simplifying framework for some technical quantum field theory work realized by some of the authors. Most notably, an important but technical parameter naturally translates to vertices at the level of maps. We also give a combinatorial proof to a formula which previously resulted from a technical recurrence, and with similar ideas we prove a conjecture of Hihn. Independently, we revisit an equation due to Arquès and Béraud for the generating function counting rooted maps with respect to edges and vertices, giving a new bijective interpretation of this equation directly on indecomposable chord diagrams, which moreover can be specialized to connected diagrams and refined to incorporate the number of crossings. Finally, we explain how these results have a simple application to the combinatorics of lambda calculus, verifying the conjecture that a certain natural family of lambda terms is equinumerous with bridgeless maps.

scholarly journals USING COMBINATORIAL MAPS FOR ALGORITHMS ON GRAPHS

2021 ◽  
Vol 37 (3) ◽  
pp. 185-200
Author(s):  
Robert Cori
Keyword(s):  
Computer Vision ◽  
Data Structure ◽  
Formal Proofs ◽  
Combinatorial Object ◽  
Structure Representation ◽  
Combinatorial Maps ◽  
To Come

The aim of this paper is to come back to a data structure representation of graph by permutations. This originated in the years 1960-1970 by contributions due to J. Edmonds [7], A. Jacques [11], W. Tutte [22] in order to consider the embedding of a graph in a surface as a combinatorial object. Some algebraic developments where suggested in [4] and [12]. It was also used for implementation in different situation, like planarity testing by H. de Fraysseix and P. Rosenstiehl [6], computer vision by G. Damiand  and A. Dupas [5] or formal proofs by G. Gonthier [9].

scholarly journals Signatures of Combinatorial Maps

2009 ◽  
pp. 370-382 ◽  
Author(s):  
Stéphane Gosselin ◽  
Guillaume Damiand ◽  
Christine Solnon
Keyword(s):  
Combinatorial Maps

Data image fusion using combinatorial maps

2005 ◽  
Author(s):  
Kamel Bouchefra ◽  
Patrick Bonnin ◽  
Aymeric De Cabrol
Keyword(s):  
Image Fusion ◽  
Combinatorial Maps
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