scholarly journals Triangulations of cyclic polytopes

2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Steffen Oppermann ◽  
Hugh Thomas
Keyword(s):  
Cyclic Polytopes ◽  
Exchange Relation ◽  
Higher Dimensional ◽  
International Audience

International audience We give a new description of the combinatorics of triangulations of even-dimensional cyclic polytopes, and of their bistellar flips. We show that the tropical exchange relation governing the number of intersections between diagonals of a polygon and a lamination (which generalizes to arbitrary surfaces) can also be generalized in a different way, to the setting of higher dimensional cyclic polytopes. Nous donnons une nouvelle description de la combinatoire des triangulations des polytopes cycliques, et de leurs mouvements bistellaires. Nous démontrons que la relation d’échange qui gouverne le nombre d'intersections entre les diagonaux d'une polygone et une lamination (qui peut être généralisée à une surface arbitraire) peut également être généralisée au cadre des polytopes cycliques.

scholarly journals Many neighborly inscribed polytopes and Delaunay triangulations

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Bernd Gonska ◽  
Arnau Padrol
Keyword(s):  
Lower Bound ◽  
Large Family ◽  
Delaunay Triangulations ◽  
Cyclic Polytopes ◽  
Point Configurations ◽  
International Audience

International audience We present a very simple explicit technique to generate a large family of point configurations with neighborly Delaunay triangulations. This proves that there are superexponentially many combinatorially distinct neighborly $d$-polytopes with $n$ vertices that admit realizations inscribed on the sphere. These are the first examples of inscribable neighborly polytopes that are not cyclic polytopes, and provide the current best lower bound for the number of combinatorial types of inscribable polytopes (and thus also of Delaunay triangulations). It coincides with the current best lower bound for the number of combinatorial types of polytopes. Nous présentons une technique explicite simple pour générer une large famille de configurations de points dont les triangulations de Delaunay sontneighborly. Cela prouve que le nombre de $d$-polytopes combinatoirement distincts avec $n$ sommets et admettant une réalisation inscrite sur la sphère est surexponentiel. Ce sont les premiers exemples de polytopes inscriptibles neighborly qui ne sont pas des polytopes cycliques et ils donnent la meilleure borne inférieure actuelle pour le nombre de types combinatoires de polytopes inscriptibles (et donc aussi de triangulations de Delaunay). Cette borne coïncide avec la meilleure borne inférieure actuelle pour le nombre de types combinatoires de polytopes.

scholarly journals Polytopes from Subgraph Statistics

2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Alexander Engström ◽  
Patrik Norén
Keyword(s):  
Exponential Random Graph Models ◽  
Schur Polynomials ◽  
Graph Models ◽  
Selberg Integral ◽  
General Picture ◽  
Cyclic Polytopes ◽  
Random Graph Models ◽  
Exponential Random Graph ◽  
Nous Trouvons ◽  
International Audience

International audience We study polytopes that are convex hulls of vectors of subgraph densities. Many graph theoretical questions can be expressed in terms of these polytopes, and statisticians use them to understand exponential random graph models. Relations among their Ehrhart polynomials are described, their duals are applied to certify that polynomials are non-negative, and we find some of their faces. For the general picture we inscribe cyclic polytopes in them and calculate volumes. From the volume calculations we conjecture that a variation of the Selberg integral indexed by Schur polynomials has a combinatorial formula. We inscribe polynomially parametrized sets, called curvy zonotopes, in the polytopes and show that they approximate the polytopes arbitrarily close. Nous étudions les polytopes qui sont les enveloppes convexes des vecteurs des densités de sous-graphe. Beaucop de questions théoriques de graphe peuvent être exprimées en termes de ces polytopes, et les statisticiens les utilisent pour comprendre les modèles de graphes aléatoires exponentielles Des relations parmi leurs polynômes d'Ehrhart sont décrites leurs duals sont appliqués pour certifier que les polynômes sont non négatifs, et nous trouvons certaines de leurs faces. Pour la description générale nous inscrivons les polytopes cycliques dans eux et calculons les volumes. D'après les calculs de volume, nous conjecturons qu'une variation de l'intégrale de Selberg indexés par des polynômes de Schur a une formule combinatoire. Nous inscrivons polynomialement les ensembles paramétrisés appelés ``curvy zonotopes'' dans les polytopes et montrons qu'ils sont arbitrairement proches de polytopes.

scholarly journals Defining amplituhedra and Grassmann polytopes

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Steven N. Karp
Keyword(s):  
Dimensional Subspace ◽  
Equivalent Condition ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Positivity Condition ◽  
Yang Mills ◽  
Cyclic Polytopes ◽  
Plücker Coordinates ◽  
International Audience ◽  
Necessary And Sufficient

International audience The totally nonnegative Grassmannian Gr≥0 k,n is the set of k-dimensional subspaces V of Rn whose nonzero Plucker coordinates all have the same sign. In their study of scattering amplitudes in N = 4 supersym- metric Yang-Mills theory, Arkani-Hamed and Trnka (2013) considered the image (called an amplituhedron) of Gr≥0 k,n under a linear map Z : Rn → Rr, where k ≤ r and the r × r minors of Z are all positive. One reason they required this positivity condition is to ensure that the map Gr≥0 k,n → Grk,r induced by Z is well defined, i.e. it takes everynelement of Gr≥0 k,n to a k-dimensional subspace of Rr. Lam (2015) gave a sufficient condition for the induced map Gr≥0 k,n → Grk,r to be well defined, in which case he called the image a Grassmann polytope. (In the case k = 1, Grassmann polytopes are just polytopes, and amplituhedra are cyclic polytopes.) We give a necessary and sufficient condition for the induced map Gr≥0 k,n → Grk,r to be well defined, in terms of sign variation. Using previous work we presented at FPSAC 2015, we obtain an equivalent condition in terms of the r × r minors of Z (assuming Z has rank r).

scholarly journals Resonance in orbits of plane partitions

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Kevin Dilks ◽  
Oliver Pechenik ◽  
Jessica Striker
Keyword(s):  
Dynamical Systems ◽  
Discrete Dynamical Systems ◽  
Plane Partitions ◽  
Higher Dimensional ◽  
International Audience ◽  
K Promotion

International audience We introduce a new concept of resonance on discrete dynamical systems. Our main result is an equivariant bijection between plane partitions in a box under rowmotion and increasing tableaux under K-promotion, using a generalization of the equivariance of promotion and rowmotion [J. Striker–N. Williams '12] to higher dimensional lattices. This theorem implies new results for K-promotion and new proofs of previous results on plane partitions.

scholarly journals Symmetries of Monocoronal Tilings

2015 ◽  
Vol Vol. 17 no.2 (Combinatorics) ◽  
Author(s):  
Dirk Frettlöh ◽  
Alexey Garber
Keyword(s):  
Euclidean Space ◽  
Euclidean Plane ◽  
Dimensional Euclidean Space ◽  
Symmetry Groups ◽  
Translation Group ◽  
One Dimensional ◽  
Higher Dimensional ◽  
International Audience

International audience The vertex corona of a vertex of some tiling is the vertex together with the adjacent tiles. A tiling where all vertex coronae are congruent is called monocoronal. We provide a classification of monocoronal tilings in the Euclidean plane and derive a list of all possible symmetry groups of monocoronal tilings. In particular, any monocoronal tiling with respect to direct congruence is crystallographic, whereas any monocoronal tiling with respect to congruence (reflections allowed) is either crystallographic or it has a one-dimensional translation group. Furthermore, bounds on the number of the dimensions of the translation group of monocoronal tilings in higher dimensional Euclidean space are obtained.

Somethin’ about Scandinavia: Danish Shorts on the Post-war International Scene

2018 ◽  
Author(s):  
C. Claire Thomson
Keyword(s):  
United Nations ◽  
International Collaboration ◽  
Marshall Plan ◽  
The Third ◽  
Animated Film ◽  
International Audience ◽  
Post War ◽  
Nordic Cooperation

Building on the picture of post-war Anglo-Danish documentary collaboration established in the previous chapter, this chapter examines three cases of international collaboration in which Dansk Kulturfilm and Ministeriernes Filmudvalg were involved in the late 1940s and 1950s. They Guide You Across (Ingolf Boisen, 1949) was commissioned to showcase Scandinavian cooperation in the realm of aviation (SAS) and was adopted by the newly-established United Nations Film Board. The complexities of this film’s production, funding and distribution are illustrative of the activities of the UN Film Board in its first years of operation. The second case study considers Alle mine Skibe (All My Ships, Theodor Christensen, 1951) as an example of a film commissioned and funded under the auspices of the Marshall Plan. This US initiative sponsored informational films across Europe, emphasising national solutions to post-war reconstruction. The third case study, Bent Barfod’s animated film Noget om Norden (Somethin’ about Scandinavia, 1956) explains Nordic cooperation for an international audience, but ironically exposed some gaps in inter-Nordic collaboration in the realm of film.

Conclusion

2018 ◽  
Author(s):  
Alistair Fox
Keyword(s):  
National Identity ◽  
New Zealand ◽  
Identity Formation ◽  
Essential Role ◽  
Coming Of Age ◽  
Financial Returns ◽  
Self Recognition ◽  
International Audience ◽  
National Identity Formation

The conclusion reaffirms the essential role played by cinema generally, and the coming-of-age genre in particular, in the process of national identity formation, because of its effectiveness in facilitating self-recognition and self-experience through a process of triangulation made possible, for the most part, by a dialogue with some of the nation’s most iconic works of literature. This section concludes by point out the danger posed, however, by an observable trend toward generic standardization in New Zealand films motivated by a desire to appeal to an international audience out of consideration for the financial returns expected by funding bodies under current regimes.

Early Cinema in Scotland

2018 ◽  
Keyword(s):  
Social History ◽  
Small Towns ◽  
Early Cinema ◽  
Popular Song ◽  
Feature Film ◽  
Local Newspapers ◽  
The Social ◽  
Production History ◽  
History Of ◽  
International Audience

This collection of essays, drawn from a three-year AHRC research project, provides a detailed context for the history of early cinema in Scotland from its inception in 1896 till the arrival of sound in the early 1930s. It details the movement from travelling fairground shows to the establishment of permanent cinemas, and from variety and live entertainment to the dominance of the feature film. It addresses the promotion of cinema as a socially ‘useful’ entertainment, and, distinctively, it considers the early development of cinema in small towns as well as in larger cities. Using local newspapers and other archive sources, it details the evolution and the diversity of the social experience of cinema, both for picture goers and for cinema staff. In production, it examines the early attempts to establish a feature film production sector, with a detailed production history of Rob Roy (United Films, 1911), and it records the importance, both for exhibition and for social history, of ‘local topicals’. It considers the popularity of Scotland as an imaginary location for European and American films, drawing their popularity from the international audience for writers such as Walter Scott and J.M. Barrie and the ubiquity of Scottish popular song. The book concludes with a consideration of the arrival of sound in Scittish cinemas. As an afterpiece, it offers an annotated filmography of Scottish-themed feature films from 1896 to 1927, drawing evidence from synopses and reviews in contemporary trade journals.

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