scholarly journals A Poset Classifying Non-Commutative Term Orders

2001 ◽  
Vol DMTCS Proceedings vol. AA,... (Proceedings) ◽  
Author(s):  
Jan Snellman
Keyword(s):  
Free Monoid ◽  
International Audience ◽  
Standard Term ◽  
Term Orders

International audience We study a poset $\Re$ on the free monoid (X*) on a countable alphabet X.This poset is determined by the fact that its total extensions are precisely the standard term orders on X*. We also investigate the poset classifying degree-compatible standard term orders, and the poset classifying sorted term orders. For the latter poset, we give a Galois coconnection with the Young lattice.

scholarly journals On morphisms preserving infinite Lyndon words

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Gwenael Richomme
Keyword(s):  
Free Monoid ◽  
Infinite Words ◽  
International Audience ◽  
Lyndon Words

International audience In a previous paper, we characterized free monoid morphisms preserving finite Lyndon words. In particular, we proved that such a morphism preserves the order on finite words. Here we study morphisms preserving infinite Lyndon words and morphisms preserving the order on infinite words. We characterize them and show relations with morphisms preserving Lyndon words or the order on finite words. We also briefly study morphisms preserving border-free words and those preserving the radix order.

scholarly journals Contextual partial commutations

2010 ◽  
Vol Vol. 12 no. 4 ◽  
Author(s):  
Christian Choffrut ◽  
Robert Mercas
Keyword(s):  
Cross Sections ◽  
Free Monoid ◽  
Special Issue ◽  
Closure Properties ◽  
Combinatorial Description ◽  
Different Types ◽  
International Audience ◽  
Congruence Classes

special issue dedicated to the second edition of the conference AutoMathA: from Mathematics to Applications International audience We consider the monoid T with the presentation < a, b; aab = aba > which is ''close'' to trace monoids. We prove two different types of results. First, we give a combinatorial description of the lexicographically minimum and maximum representatives of their congruence classes in the free monoid \a, b\* and solve the classical equations, such as commutation and conjugacy in T. Then we study the closure properties of the two subfamilies of the rational subsets of T whose lexicographically minimum and maximum cross-sections respectively, are rational in \a, b\*.

scholarly journals Rationality, irrationality, and Wilf equivalence in generalized factor order

2009 ◽  
Vol DMTCS Proceedings vol. AK,... (Proceedings) ◽  
Author(s):  
Sergey Kitaev ◽  
Jeffrey Liese ◽  
Jeffrey Remmel ◽  
Bruce Sagan
Keyword(s):  
Generating Function ◽  
Free Monoid ◽  
Recursive Formula ◽  
Finite State Automaton ◽  
Finite State ◽  
Pumping Lemma ◽  
International Audience ◽  
Wilf Equivalence ◽  
Positive Integers ◽  
Factor Order

International audience Let $P$ be a partially ordered set and consider the free monoid $P^{\ast}$ of all words over $P$. If $w,w' \in P^{\ast}$ then $w'$ is a factor of $w$ if there are words $u,v$ with $w=uw'v$. Define generalized factor order on $P^{\ast}$ by letting $u \leq w$ if there is a factor $w'$ of $w$ having the same length as $u$ such that $u \leq w'$, where the comparison of $u$ and $w'$ is done componentwise using the partial order in $P$. One obtains ordinary factor order by insisting that $u=w'$ or, equivalently, by taking $P$ to be an antichain. Given $u \in P^{\ast}$, we prove that the language $\mathcal{F}(u)=\{w : w \geq u\}$ is accepted by a finite state automaton. If $P$ is finite then it follows that the generating function $F(u)=\sum_{w \geq u} w$ is rational. This is an analogue of a theorem of Björner and Sagan for generalized subword order. We also consider $P=\mathbb{P}$, the positive integers with the usual total order, so that $\mathbb{P}^{\ast}$ is the set of compositions. In this case one obtains a weight generating function $F(u;t,x)$ by substituting $tx^n$ each time $n \in \mathbb{P}$ appears in $F(u)$. We show that this generating function is also rational by using the transfer-matrix method. Words $u,v$ are said to be Wilf equivalent if $F(u;t,x)=F(v;t,x)$ and we can prove various Wilf equivalences combinatorially. Björner found a recursive formula for the Möbius function of ordinary factor order on $P^{\ast}$. It follows that one always has $\mu (u,w)=0, \pm 1$. Using the Pumping Lemma we show that the generating function $M(u)= \sum_{w \geq u} | \mu (u,w) | w$ can be irrational. Soit $P$ un ensemble partiellement ordonné. Nous considérons le monoïde libre $P^{\ast}$ de tous les mots utilisant $P$ comme alphabet. Si $w,w' \in P^{\ast}$, on dit que $w'$ est un facteur de $w$ s'il y a des mots $u,v$ avec $w=uw'v$. Nous définissons l'ordre facteur généralisé sur $P^{\ast}$ par: $u \leq w$ s'il y a un facteur $w'$ de $w$ ayant la même longueur que $u$ tel que $u \leq w'$, où la comparaison de $u$ avec $w'$ est faite lettre par lettre utilisant l'ordre en $P$. On obtient l'ordre facteur usuel si on insiste que $u=w'$ ou, ce qui est la même chose, en prenant $P$ comme antichaîne. Pour n'importe quel $u \in P^{\ast}$, nous démontrons que le langage $\mathcal{F}(u)=\{w : w \geq u\}$ est accepté par un automaton avec un nombre fini d'états. Si $P$ est fini, ça implique que la fonction génératrice $F(u)=\sum_{w \geq u} w$ est rationnelle. Björner et Sagan ont démontré le théorème analogue pour l'ordre où, en la définition au-dessus, $w'$ est un sous-mot de $w$. Nous considérons aussi le cas $P=\mathbb{P}$, les entiers positifs avec l'ordre usuel, donc $P^{\ast}$ est l'ensemble des compositions. En ce cas on obtient une fonction génératrice pondéré $F(u;t,x)$ en remplaçant $tx^n$ chaque fois on trouve $n \in \mathbb{P}$ en $F(u)$. Nous démontrons que cette fonction génératrice est aussi rationnelle en utilisant la Méthode Matrice de Tranfert. On dit que let mots $u,v$ sont Wilf-équivalents si $F(u;t,x)=F(v;t,x)$. Nous pouvons démontré quelques équivalences dans une manière combinatoire. Björner a trouvé une formule récursive pour la fonction Möbius de l'ordre facteur usuel sur $P^{\ast}$. Cette formule implique qu'on a toujours $\mu (u,w)=0, \pm 1$. En utilisant le Lemme de Pompage, nous démontrons que la fonction génératrice $M(u)= \sum_{w \geq u} | \mu (u,w) | w$ peut être irrationnelle.

scholarly journals Toric Ideals of Flow Polytopes

2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Matthias Lenz
Keyword(s):  
Gröbner Bases ◽  
Grobner Bases ◽  
Toric Ideals ◽  
Toric Ideal ◽  
Birkhoff Polytope ◽  
Flow Polytopes ◽  
International Audience ◽  
Transportation Polytopes ◽  
Term Orders ◽  
Special Case

International audience We show that toric ideals of flow polytopes are generated in degree $3$. This was conjectured by Diaconis and Eriksson for the special case of the Birkhoff polytope. Our proof uses a hyperplane subdivision method developed by Haase and Paffenholz. It is known that reduced revlex Gröbner bases of the toric ideal of the Birkhoff polytope $B_n$ have at most degree $n$. We show that this bound is sharp for some revlex term orders. For $(m \times n)$-transportation polytopes, a similar result holds: they have Gröbner bases of at most degree $\lfloor mn/2 \rfloor$. We construct a family of examples, where this bound is sharp. Nous démontrons que les idéaux toriques des polytopes de flot sont engendrés par un ensemble de degré $3$. Cela a été conjecturé par Diaconis et Eriksson pour le cas particulier du polytope de Birkhoff. Notre preuve utilise une méthode de subdivision par hyperplans, développée par Haase et Paffenholz. Il est bien connu que les bases de Gröbner revlex réduite du polytope de Birkhoff $B_n$ sont au plus de degré $n$. Nous démontrons que cette borne est optimale pour quelques ordres revlex. Pour les polytopes de transportation de dimension $(m \times n)$, il existe un résultat similaire : leurs bases de Gröbner sont au plus de degré $\lfloor mn/2 \rfloor$. Nous construisons une famille d'exemples pour lesquels cette borne est atteinte.

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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