scholarly journals Fourientation activities and the Tutte polynomial

2020 ◽  
Vol DMTCS Proceedings, 28th... ◽  
Author(s):  
Spencer Backman ◽  
Sam Hopkins ◽  
Lorenzo Traldi

International audience A fourientation of a graph G is a choice for each edge of the graph whether to orient that edge in either direction, leave it unoriented, or biorient it. We may naturally view fourientations as a mixture of subgraphs and graph orientations where unoriented and bioriented edges play the role of absent and present subgraph edges, respectively. Building on work of Backman and Hopkins (2015), we show that given a linear order and a reference orientation of the edge set, one can define activities for fourientations of G which allow for a new 12 variable expansion of the Tutte polynomial TG. Our formula specializes to both an orientation activities expansion of TG due to Las Vergnas (1984) and a generalized activities expansion of TG due to Gordon and Traldi (1990).

2010 ◽  
Vol DMTCS Proceedings vol. AM,... (Proceedings) ◽  
Author(s):  
Thomas Fernique ◽  
Damien Regnault

International audience This paper introduces a Markov process inspired by the problem of quasicrystal growth. It acts over dimer tilings of the triangular grid by randomly performing local transformations, called $\textit{flips}$, which do not increase the number of identical adjacent tiles (this number can be thought as the tiling energy). Fixed-points of such a process play the role of quasicrystals. We are here interested in the worst-case expected number of flips to converge towards a fixed-point. Numerical experiments suggest a $\Theta (n^2)$ bound, where $n$ is the number of tiles of the tiling. We prove a $O(n^{2.5})$ upper bound and discuss the gap between this bound and the previous one. We also briefly discuss the average-case.


2018 ◽  
Vol 3 (1) ◽  
pp. 28
Author(s):  
Chenchen Xu ◽  
Yen-Hwei Lin ◽  
Karthik Durvasula

Two analyses, vowel sonority and the linear order of pre-contraction vowels, have been proposed to account for the vowel selection between two competing vowels in Chinese syllable contraction. An experiment was run to test whether sonority and/or linear order bias the vowel selection in Rugao syllable contraction. Our results confirmed the role of vowel sonority, and did not present supporting evidence for the linear order analysis. Sonority hierarchies along the dimensions of both height and centrality exhibit the same consistent and robust pattern, providing a new perspective to look at competing vowels in vowel-related phonological processes.


1990 ◽  
Vol 15 (3) ◽  
pp. 223-233 ◽  
Author(s):  
Bridget Jones

In any consideration of theatre in the French Caribbean, the name Césaire is bound to be mentioned. Aimé Césaire's La Tragédie du roi Christophe (1963) is the most widely- known play in French by a black dramatist, and is now even in the repertoire of the Comédie-Française, and his plays figure widely in checklists of ‘African’ theatre. A revealing contrast can be made between the epic dramas of Aimé Césaire, written for an international audience, especially the newly independent black nations of the 1960s, and the work of his daughter, Ina. He tackles from the standpoint of Négritude major themes of historical drama: the nature of sovereignty, the forging of nationhood; he storms the heights of tragic poetry in French. She is attentive, not to the lonely hero constructing his Haitian Citadel of rock, but to the Creole voices of the grassroots. She brings to the stage the lives of ordinary women, the lore and legends that sustained the slaves and their descendants. Her achievement should of course be assessed away from her father's shadow, but the ‘divergent orientation of the two generations’ also suggests the greater confidence today in the role of Creole language and oral literature, and in a serious theatre within Martinique.


Lingua ◽  
2013 ◽  
Vol 136 ◽  
pp. 125-144 ◽  
Author(s):  
Peter W. Culicover
Keyword(s):  

Slovo ◽  
2020 ◽  
Vol How to think of literary... ◽  
Author(s):  
Tamara Svanidzé

International audience The present work questions the logic and the functioning of the flows of importation in the field of literature in the second half of the 19th century, using the concept of cultural transfers, as developed by Michel Espagne and Michael Werner, along with Pierre Bourdieu’s concept of the literary field. These methodological perspectives allow us to relativize the canonical vision of Georgian literature and to illuminate the role played by the importation of European works in the organization and evolution of the internal literary field. My analysis of critical discourse and of paratexts reveals how much literary transfers enabled Georgian literature to renew itself and actively participated in the configuration of the host system, while at the same time contributing to the reinforcement of the positions that structure the Georgian intellectual field of the time. This field has witnessed the arrival of a new conception of literature conveyed by the reformist intelligentsia that relegates traditional practices to the periphery of the system, and and has become divided between literature in conformity with aesthetic norms and current ideologies and the “sub‑field.” By clarifying the motivations that have led to the selection and interpretation of European texts and authors, I hope to offer a better comprehensive perspective on the different facets of this field and on the power relations that constitute it. Le présent travail contribue à la relecture de l’histoire de la littérature géorgienne en interrogeant le fonctionnement et les logiques des flux d’importation dans le domaine de la littérature en Géorgie dans la seconde moitié du xixe siècle à l’aide du concept des transferts culturels élaboré par Michel Espagne et Michel Werner et de la notion du champ littéraire développé par Pierre Bourdieu. Ces perspectives méthodologiques permettent de relativiser la vision canonique de la littérature géorgienne et d’éclairer le rôle joué par l’importation des œuvres européennes dans l’organisation et l’évolution du champ littéraire interne. En effet, l’analyse des discours critiques et des paratextes révèle combien les transferts littéraires ont permis à la littérature géorgienne de se renouveler et ont participé activement à la configuration du système d’accueil, en contribuant au renforcement des positions qui structuraient le champ intellectuel géorgien de l’époque. Celui-ci connaît l’avènement d’une nouvelle conception de la littérature véhiculée par l’intelligentsia réformiste qui relègue les pratiques traditionnelles à la périphérie du système, et se voit partagé entre la littérature en accord avec les normes esthétiques et idéologiques en vigueur et le « sous-champ ». Ainsi, élucider les motivations qui ont conduit à la sélection et aux interprétations des textes et des auteurs européens offre une meilleure image globale des différentes facettes de ce champ et des rapports de force qui le constituent. სტატიის მიზანია თარგმანების როლის განსაზღვრა xix საუკუნის ქართული ლიტერატურული სივრცის ფორმირებაში. კვლევის მეთოდოლოგიურ საფუძვლად გამოყენებულია ბურდიეს (Pierre Bourdieu) ლიტერატურული ველის კონცეფტი და ესპანისა (Michel Espagne) და ვერნერის (Michael Werner) მიერ შემუშავებულ კულტურული ტრანსფერის თეორია, რომლის მიხედვითაც, კულტურული ტრანსფერები უნდა განიხილებოდეს აკულტურაციის ფენომენზე დაყრდნობით და კულტურული გავლენის პარადიგმის გვერდის ავლით, ანუ მიმღები კულტურის სპეციფიკაზე ყურადღების გამახვილებით. მათი საშუალებით განვავითარეთ ჰიპოთეზა, რომ ქართული ინტელექტუქლური ველი ჩამოყალიბდა უცხოური ელემენტების სესხებით და ეს სესხება არ ნიშნავს მარტივ იმიტაციას არამედ სელექციის, ადაფტაციისა და ტრანსფორმაციის მთელ პროცესებს. გარდა ამისა, განვიხილეთ ქართული ლიტერატურული ველის შიდა დინამიკა, კერძოდ, როგორ ახდენდნენ საზოგადოებრივ-პოლიტიკური ჯგუფები ევროპელი ავტორების მოხმობით სიმბოლურად დომინანტური პოზიციის დაკავებასა და გამყარებას.


2010 ◽  
Vol DMTCS Proceedings vol. AN,... (Proceedings) ◽  
Author(s):  
Luca Moci

International audience We introduce a multiplicity Tutte polynomial $M(x,y)$, which generalizes the ordinary one and has applications to zonotopes and toric arrangements. We prove that $M(x,y)$ satisfies a deletion-restriction recurrence and has positive coefficients. The characteristic polynomial and the Poincaré polynomial of a toric arrangement are shown to be specializations of the associated polynomial $M(x,y)$, likewise the corresponding polynomials for a hyperplane arrangement are specializations of the ordinary Tutte polynomial. Furthermore, $M(1,y)$ is the Hilbert series of the related discrete Dahmen-Micchelli space, while $M(x,1)$ computes the volume and the number of integral points of the associated zonotope. On introduit un polynôme de Tutte avec multiplicité $M(x, y)$, qui généralise le polynôme de Tutte ordinaire et a des applications aux zonotopes et aux arrangements toriques. Nous prouvons que $M(x, y)$ satisfait une récurrence de "deletion-restriction'' et a des coefficients positifs. Le polynôme caractéristique et le polynôme de Poincaré d'un arrangement torique sont des spécialisations du polynôme associé $M(x, y)$, de même que les polynômes correspondants pour un arrangement d'hyperplans sont des spécialisations du polynôme de Tutte ordinaire. En outre, $M(1, y)$ est la série de Hilbert de l'espace discret de Dahmen-Micchelli associé, et $M(x, 1)$ calcule le volume et le nombre de points entiers du zonotope associé.


2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Petter Brändèn ◽  
Luca Moci

International audience We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two. We provide a generalized Fortuin-Kasteleyn representation for representable arithmetic matroids, with applications to arithmetic colorings and flows. We give a new proof of the positivity of the coefficients of the arithmetic Tutte polynomial in the more general framework of pseudo-arithmetic matroids. In the case of a representable arithmetic matroid, we provide a geometric interpretation of the coefficients of the arithmetic Tutte polynomial. Nous introduisons une version arithmétique du polynôme de Tutte multivariée récemment étudié par Sokal, et un quasi-polynôme qui interpole entre les deux. Nous proposons une représentation de Fortuin-Kasteleyn neutralise pour les matroïdes arithmétiques représentables, avec des applications aux colorations et flux arithmétiques. Nous donnons une nouvelle preuve de la positivité des coefficients du polynôme de Tutte arithmétique dans le cadre plus général des matroïdes pseudo-arithmétiques. Dans le cas d'un matroïde arithmétique représentable, nous proposons une interprétation géométrique des coefficients du polynôme de Tutte arithmétique.


2012 ◽  
Vol DMTCS Proceedings vol. AR,... (Proceedings) ◽  
Author(s):  
Matjaž Konvalinka ◽  
Igor Pak

International audience Cayley polytopes were defined recently as convex hulls of Cayley compositions introduced by Cayley in 1857. In this paper we resolve Braun's conjecture, which expresses the volume of Cayley polytopes in terms of the number of connected graphs. We extend this result to a two-variable deformations, which we call Tutte polytopes. The volume of the latter is given via an evaluation of the Tutte polynomial of the complete graph. Our approach is based on an explicit triangulation of the Cayley and Tutte polytope. We prove that simplices in the triangulations correspond to labeled trees and forests. The heart of the proof is a direct bijection based on the neighbors-first search graph traversal algorithm. Les polytopes de Cayley ont été définis récemment comme des ensembles convexes de compositions de Cayley introduits par Cayley en 1857. Dans ce papier, nous résolvons la conjecture de Braun. Cette dernière exprime le volume du polytopes de Cayley en termes du nombre de graphes connexes. Nous étendons ce résultat à des déformations de polytopes de Cayley à deux variables, à savoir les polytopes de Tutte. Le volume de ces derniers est donnè par une évaluation du polynôme de Tutte du graphe complet. Notre approche est basée sur une triangulation explicite des polytopes de Cayley et Tutte. Nous démontrons que les simplexes de ces triangulations correspondent à des arbres marqués. La pierre angulaire de notre démonstration est une bijection directe basées sur l'algorithme de la recherche du premier voisin sur le graphe.


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