scholarly journals A de Bruijn - Erdos theorem and metric spaces

2011 ◽  
Vol Vol. 13 no. 1 (Combinatorics) ◽  
Author(s):  
Ehsan Chiniforooshan ◽  
Vasek Chvatal
Keyword(s):  
Metric Spaces ◽  
International Audience ◽  
De Bruijn

Combinatorics International audience De Bruijn and Erdos proved that every noncollinear set of n points in the plane determines at least n distinct lines. Chen and Chvatal suggested a possible generalization of this theorem in the framework of metric spaces. We provide partial results in this direction.

scholarly journals The number of Euler tours of a random $d$-in/$d$-out graph

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Páidí Creed ◽  
Mary Cryan
Keyword(s):  
Asymptotic Distribution ◽  
Directed Graph ◽  
Polynomial Time ◽  
Simple Approach ◽  
Uniform Sampling ◽  
Concentration Result ◽  
International Audience ◽  
De Bruijn ◽  
Euler Tours

International audience In this paper we obtain the expectation and variance of the number of Euler tours of a random $d$-in/$d$-out directed graph, for $d \geq 2$. We use this to obtain the asymptotic distribution and prove a concentration result. We are then able to show that a very simple approach for uniform sampling or approximately counting Euler tours yields algorithms running in expected polynomial time for almost every $d$-in/$d$-out graph. We make use of the BEST theorem of de Bruijn, van Aardenne-Ehrenfest, Smith and Tutte, which shows that the number of Euler tours of a $d$-in/$d$-out graph is the product of the number of arborescences and the term $[(d-1)!]^n/n$. Therefore most of our effort is towards estimating the asymptotic distribution of the number of arborescences of a random $d$-in/$d$-out graph.

scholarly journals An Algebraic Analogue of a Formula of Knuth

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Lionel Levine
Keyword(s):  
Directed Graph ◽  
Spanning Trees ◽  
Line Graph ◽  
Torsion Subgroup ◽  
Directed Line ◽  
De Bruijn Graphs ◽  
International Audience ◽  
De Bruijn ◽  
Kautz Graphs ◽  
Sandpile Group

International audience We generalize a theorem of Knuth relating the oriented spanning trees of a directed graph $G$ and its directed line graph $\mathcal{L} G$. The sandpile group is an abelian group associated to a directed graph, whose order is the number of oriented spanning trees rooted at a fixed vertex. In the case when $G$ is regular of degree $k$, we show that the sandpile group of $G$ is isomorphic to the quotient of the sandpile group of $\mathcal{L} G$ by its $k$-torsion subgroup. As a corollary we compute the sandpile groups of two families of graphs widely studied in computer science, the de Bruijn graphs and Kautz graphs. Nous généralisons un théorème de Knuth qui relie les arbres couvrants dirigés d'un graphe orienté $G$ au graphe adjoint orienté $\mathcal{L} G$. On peut associer à tout graphe orienté un groupe abélien appelé groupe du tas de sable, et dont l'ordre est le nombre d'arbres couvrants dirigés enracinés en un sommet fixé. Lorsque $G$ est régulier de degré $k$, nous montrons que le groupe du tas de sable de $G$ est isomorphe au quotient du groupe du tas de sable de $\mathcal{L} G$ par son sous-groupe de $k$-torsion. Comme corollaire, nous déterminons les groupes de tas de sable de deux familles de graphes étudiées en informatique: les graphes de de Bruijn et les graphes de Kautz.

scholarly journals Properties of the extremal infinite smooth words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Srečko Brlek ◽  
Guy Melançon ◽  
Geneviève Paquin
Keyword(s):  
De Bruijn Graph ◽  
Lexicographical Order ◽  
Naive Algorithm ◽  
International Audience ◽  
De Bruijn

International audience Smooth words are connected to the Kolakoski sequence. We construct the maximal and the minimal in nite smooth words, with respect to the lexicographical order. The naive algorithm generating them is improved by using a reduction of the De Bruijn graph of their factors. We also study their Lyndon factorizations. Finally, we show that the minimal smooth word over the alphabet f1; 3g belongs to the orbit of the Fibonacci word.

scholarly journals A de Bruijn-Erdős theorem for 1–2 metric spaces

2014 ◽  
Vol 64 (1) ◽  
pp. 45-51 ◽  
Author(s):  
Vašek Chvátal
Keyword(s):  
Metric Spaces ◽  
De Bruijn

scholarly journals A De Bruijn–Erdős Theorem for Chordal Graphs

10.37236/3527 ◽  
2015 ◽  
Vol 22 (1) ◽  
Author(s):  
Laurent Beaudou ◽  
Adrian Bondy ◽  
Xiaomin Chen ◽  
Ehsan Chiniforooshan ◽  
Maria Chudnovsky ◽  
...  
Keyword(s):  
Metric Spaces ◽  
Chordal Graphs ◽  
Combinatorial Theorem ◽  
De Bruijn ◽  
Special Case

A special case of a combinatorial theorem of De Bruijn and Erdős asserts that every noncollinear set of $n$ points in the plane determines at least $n$ distinct lines. Chen and Chávtal suggested a possible generalization of this assertion in metric spaces with appropriately defined lines. We prove this generalization in all metric spaces induced by connected chordal graphs.

scholarly journals The height of watermelons with wall - Extended Abstract

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Thomas Feierl
Keyword(s):  
Average Height ◽  
Height Distribution ◽  
Famous Result ◽  
Plane Trees ◽  
International Audience ◽  
De Bruijn

International audience We derive asymptotics for the moments of the height distribution of watermelons with $p$ branches with wall. This generalises a famous result by de Bruijn, Knuth and Rice on the average height of planted plane trees, and a result by Fulmek on the average height of watermelons with two branches.

scholarly journals Number of cycles in the graph of $312$-avoiding permutations

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Richard Ehrenborg ◽  
Sergey Kitaev ◽  
Einar Steingrımsson
Keyword(s):  
Nous Avons ◽  
De Bruijn Graph ◽  
International Audience ◽  
De Bruijn ◽  
Affine Permutations ◽  
Number Of Cycles

International audience The graph of overlapping permutations is defined in a way analogous to the De Bruijn graph on strings of symbols. However, instead of requiring the tail of one permutation to equal the head of another for them to be connected by an edge, we require that the head and tail in question have their letters appear in the same order of size. We give a formula for the number of cycles of length $d$ in the subgraph of overlapping $312$-avoiding permutations. Using this we also give a refinement of the enumeration of $312$-avoiding affine permutations. Le graphique de permutations qui se chevauchent est définie d’une manière analogue à celle du graphe de De Bruijn sur des chaînes de symboles. Cependant, au lieu d’exiger la queue d’une permutation d’égaler la tête d’un autre pour qu’ils soient reliés par un bord, nous avons besoin que la tête et la queue en question ont leurs lettres apparaissent dans le même ordre de grandeur. Nous donnons une formule pour le nombre de cycles de longueur$d$ dans le sous- graphe de chevauchement $312$-évitant permutations. L’utilisation de ce nous donnent également un raffinement de l’énumération de$312$-évitant permutations affines.

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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