scholarly journals A bijection for rooted maps on general surfaces (extended abstract)

2015 ◽  
Vol DMTCS Proceedings, 27th... (Proceedings) ◽  
Author(s):  
Guillaume Chapuy ◽  
Maciej Dołęga

International audience We extend the Marcus-Schaeffer bijection between orientable rooted bipartite quadrangulations (equivalently: rooted maps) and orientable labeled one-face maps to the case of all surfaces, orientable or non-orientable. This general construction requires new ideas and is more delicate than the special orientable case, but carries the same information. It thus gives a uniform combinatorial interpretation of the counting exponent $\frac{5(h-1)}{2}$ for both orientable and non-orientable maps of Euler characteristic $2-2h$ and of the algebraicity of their generating functions. It also shows the universality of the renormalization factor $n$<sup>&frac14;</sup> for the metric of maps, on all surfaces: the renormalized profile and radius in a uniform random pointed bipartite quadrangulation of size $n$ on any fixed surface converge in distribution. Finally, it also opens the way to the study of Brownian surfaces for any compact 2-dimensional manifold. Nous étendons la bijection de Marcus et Schaeffer entre quadrangulations biparties orientables (de manière équivalente: cartes enracinées) et cartes à une face étiquetées orientables à toutes les surfaces, orientables ou non. Cette construction générale requiert des idées nouvelles et est plus délicate que dans le cas particulier orientable, mais permet des utilisations similaires. Elle donne donc une interprétation combinatoire uniforme de l’exposant de comptage $\frac{5(h-1)}{2}$ pour les cartes orientables et non-orientables de caractéristique d’Euler $2-2h$, et de l’algébricité des fonctions génératrices. Elle montre l’universalité du facteur de normalisation $n$<sup>&frac14;</sup> pour la métrique des cartes, sur toutes les surfaces: le profil et le rayon d’une quadrangulation enracinée pointée sur une surface fixée converge en distribution. Enfin, elle ouvre à la voie à l’étude des surfaces Browniennes pour toute 2-variété compacte.

2013 ◽  
Vol DMTCS Proceedings vol. AS,... (Proceedings) ◽  
Author(s):  
Jair Taylor

International audience We develop a method for counting words subject to various restrictions by finding a combinatorial interpretation for a product of formal sums of Laguerre polynomials. We use this method to find the generating function for $k$-ary words avoiding any vincular pattern that has only ones. We also give generating functions for $k$-ary words cyclically avoiding vincular patterns with only ones whose runs of ones between dashes are all of equal length, as well as the analogous results for compositions. Nous développons une méthode pour compter des mots satisfaisants certaines restrictions en établissant une interprétation combinatoire utile d’un produit de sommes formelles de polynômes de Laguerre. Nous utilisons cette méthode pour trouver la série génératrice pour les mots $k$-aires évitant les motifs vinculars consistant uniquement de uns. Nous présentons en suite les séries génératrices pour les mots $k$-aires évitant de façon cyclique les motifs vinculars consistant uniquement de uns et dont chaque série de uns entre deux tirets est de la même longueur. Nous présentons aussi les résultats analogues pour les compositions.


2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Miles Eli Jones ◽  
Jeffrey Remmel

International audience In this paper, we develop a new method to compute generating functions of the form $NM_τ (t,x,y) = \sum\limits_{n ≥0} {\frac{t^n} {n!}}∑_{σ ∈\mathcal{lNM_{n}(τ )}} x^{LRMin(σ)} y^{1+des(σ )}$ where $τ$ is a permutation that starts with $1, \mathcal{NM_n}(τ )$ is the set of permutations in the symmetric group $S_n$ with no $τ$ -matches, and for any permutation $σ ∈S_n$, $LRMin(σ )$ is the number of left-to-right minima of $σ$ and $des(σ )$ is the number of descents of $σ$ . Our method does not compute $NM_τ (t,x,y)$ directly, but assumes that $NM_τ (t,x,y) = \frac{1}{/ (U_τ (t,y))^x}$ where $U_τ (t,y) = \sum_{n ≥0} U_τ ,n(y) \frac{t^n}{ n!}$ so that $U_τ (t,y) = \frac{1}{ NM_τ (t,1,y)}$. We then use the so-called homomorphism method and the combinatorial interpretation of $NM_τ (t,1,y)$ to develop recursions for the coefficient of $U_τ (t,y)$. Dans cet article, nous développons une nouvelle méthode pour calculer les fonctions génératrices de la forme $NM_τ (t,x,y) = \sum\limits_{n ≥0} {\frac{t^n} {n!}}∑_{σ ∈\mathcal{lNM_{n}(τ )}} x^{LRMin(σ)} y^{1+des(σ )}$ où τ est une permutation, $\mathcal{NM_n}(τ )$ est l'ensemble des permutations dans le groupe symétrique $S_n$ sans $τ$-matches, et pour toute permutation $σ ∈S_n$, $LRMin(σ )$ est le nombre de minima de gauche à droite de $σ$ et $des(σ )$ est le nombre de descentes de $σ$ . Notre méthode ne calcule pas $NM_τ (t,x,y)$ directement, mais suppose que $NM_τ (t,x,y) = \frac{1}{/ (U_τ (t,y))^x}$ où $U_τ (t,y) = \sum_{n ≥0} U_τ ,n(y) \frac{t^n}{ n!}$ de sorte que $U_τ (t,y) = \frac{1}{ NM_τ (t,1,y)}$. Nous utilisons ensuite la méthode dite "de l'homomorphisme'' et l'interprétation combinatoire de $NM_τ (t,1,y)$ pour développer des récursions sur le coefficient de $U_τ (t,y)$.


2021 ◽  
Vol 111 (3) ◽  
Author(s):  
Massimo Gisonni ◽  
Tamara Grava ◽  
Giulio Ruzza

AbstractWe express the topological expansion of the Jacobi Unitary Ensemble in terms of triple monotone Hurwitz numbers. This completes the combinatorial interpretation of the topological expansion of the classical unitary invariant matrix ensembles. We also provide effective formulæ for generating functions of multipoint correlators of the Jacobi Unitary Ensemble in terms of Wilson polynomials, generalizing the known relations between one point correlators and Wilson polynomials.


2003 ◽  
Vol DMTCS Proceedings vol. AC,... (Proceedings) ◽  
Author(s):  
Michel Nguyên Thê

International audience This paper gives a survey of the limit distributions of the areas of different types of random walks, namely Dyck paths, bilateral Dyck paths, meanders, and Bernoulli random walks, using the technology of generating functions only.


2011 ◽  
Vol DMTCS Proceedings vol. AO,... (Proceedings) ◽  
Author(s):  
Hoda Bidkhori

International audience In this paper we study finite Eulerian posets which are binomial or Sheffer. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows: (1) We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets; (2) We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases; (3) In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets. We also study Eulerian triangular posets. This paper answers questions posed by R. Ehrenborg and M. Readdy. This research is also motivated by the work of R. Stanley about recognizing the \emphboolean lattice by looking at smaller intervals. Nous étudions les ensembles partiellement ordonnés finis (EPO) qui sont soit binomiaux soit de type Sheffer (deux notions reliées aux séries génératrices et à la géométrie). Nos résultats sont les suivants: (1) nous déterminons la structure des EPO Euleriens et binomiaux; nous classifions ainsi les fonctions factorielles de tous ces EPO; (2) nous donnons une classification presque complète des fonctions factorielles des EPO Euleriens de type Sheffer; (3) dans la plupart de ces cas, nous déterminons complètement la structure des EPO Euleriens et Sheffer, ce qui est plus fort que classifier leurs fonctions factorielles. Nous étudions aussi les EPO Euleriens triangulaires. Cet article répond à des questions de R. Ehrenborg and M. Readdy. Il est aussi motivé par le travail de R. Stanley sur la reconnaissance du treillis booléen via l'étude des petits intervalles.


Slovo ◽  
2017 ◽  
Vol The autobiographical... (Beyond the steppes of Central...) ◽  
Author(s):  
Adeeb KHALID

International audience This a rticle explores t he s o-called “ Memoirs” o f M unavvar qori Abdurashidxon o’g’li (1878-1931), a major figure in the politics of Turkestanin the era of the revolution and an early victim of the OGPU. The autobiographical text is a series of pokazanija written while Munavvar qori was under arrest in which he describes his political activities since the revolution. The article analyses the way in which Munavvar qori presents himself—a combination limited confession with plausible denial or extenuation—and the way he deploys language. The article also presents lengthy excerpts in English translation. cette étude examine les prétendus « Mémoires » de Munavvar qori Abdurashidxon o’g’li (1878-1931), une figure d’importance dans l’histoirepolitique du Turkestan à l’ère révolutionnaire et une des premières victimes de l’OGPU. Le texte autobiographique comprend une série de pokazanija, écrits quand Munavvar qori était en état d’arrestation, et qui racontent ses activités depuis la révolution. L’étude analyse la manière avec laquelle on se présente – soit une combinaison de confession limitée et de démentis vraisemblables – et le langage qu’on y déploie. L’étude offre aussi des extraits du texte en traduction anglaise. В статье исследуется так называемые «Воспоминания» Мунаввар кори Абдурашидхонов (1878-1931 гг.), один из виднейших деятелейполитической жизни Туркестана в эпохи революции и один из ранних жертв ОГПУ. Автобиографический текст состоит из ряда показаний, написанные во время выключения автора, и в которых он запишет его деятельность в послереволюционной период. В данной статье анализируется способов, в которых Мунаввар кори представляет себя (между умеренным признанием вины и отдалением в вероятной мере из ее) и языка, котором он используется. Статья тоже содержат в себе длинных выдержки из текста на английском переводе.


Slovo ◽  
2020 ◽  
Vol How to think of literary... (Varia) ◽  
Author(s):  
Tomasz Krupa

International audience The case of Sorana Gurian (1913‑1956) allows to examine the situation of multiple exclusion in the 20th century European society: she is a Jewish woman, a stranger accused of espionage and collaboration and her body, disabled and affected by cancer, becomes the main culprit of this plural banishment. The author is a tragic figure: not only because of her life, but also due to the oblivion that her oeuvre fell into – yet original and contemporarily recognized – counting six volumes in French and Romanian and dozens of press publications. In the paper, I propose to read chosen literary chronicles commenting on two Gurian’s editions published in Romania in 1945‑1946 – Zilele nu se întorc niciodată [Days that never return] and Întâmplări între amurg și noapte [Adventures between twilight and night]. These chronicles show the way in which the Other was perceived, in this case – a woman writer, a disabled woman or a Jewish woman in the 20th century. Such perspective aims to show the non‑ aesthetic conditions (gender, corporality, social class, political convictions, ethnic origin, etc.) which have determined Gurian’s appearance and disappearance in the literary scene, and which still influence the way of perceiving her texts in Romania. At the end of this study, I reflect on the possibility of rehabilitating this figure in the history of European literature, that could renew the Romanian literary canon of the 20th century, in which women writers haven’t still found their place. Le cas de Sorana Gurian (1913-1956) permet d’examiner la situation d’une multiple exclusion au sein de la société européenne du xxe siècle : elle est à la fois femme, juive et étrangère, accusée d’espionnage et de collaboration, et son corps, handicapé et touché par le cancer, devient le principal coupable de ce bannissement pluriel. L’auteure est une figure tragique : non seulement par sa vie, mais aussi par l’oubli dans lequel est tombée son œuvre – pourtant originale et reconnue à l’époque –, comptant six volumes en roumain et en français et des dizaines de publications dans la presse. Dans le présent article, je propose une lecture de quelques chroniques littéraires portant sur deux éditions de Gurian parues en Roumanie en 1945-1946 : Zilele nu se întorc niciodată [Les jours ne reviennent jamais] et Întâmplări între amurg și noapte [Aventures entre crépuscule et nuit], qui témoignent de la manière dont on percevait l’Autre, en l’occurrence une femme écrivain, une femme infirme ou bien une femme d’origine juive au xxe siècle. Cette perspective a pour but de montrer les conditionnements autres qu’esthétiques (genre, corporalité, classe sociale, convictions politiques, origine ethnique, etc.) qui ont déterminé l’apparition et la disparition de Gurian sur la scène littéraire, et qui influencent toujours la manière de percevoir ses textes en Roumanie. À la fin de cette étude, je réfléchis à la possibilité de réhabiliter cette figure dans l’histoire de la littérature européenne, ce qui pourrait permettre de rediscuter le canon littéraire roumain du xxe siècle, où les femmes écrivains ne trouvent toujours pas leur place. Przypadek Sorany Gurian (1913‑1956) pozwala zbadać sytuację wielokrotnego wykluczenia w xx‑wiecznym społeczeństwie europejskim: jest ona jednocześnie kobietą, Żydówką, obcą, oskarżoną o szpiegostwo i kolaborację, zaś jej ciało, niepełnosprawne i chore na raka, staje się głównym winowajcą tego mnogiego wygnania. Autorka jest postacią tragiczną nie tylko ze względu na jej życie, lecz również ze względu na zapomnienie, w jakie popadła jej oryginalna i uznana przez współczesnych twórczość, na którą składają się sześć wydań w językach francuskim i rumuńskim oraz dziesiątki publikacji w prasie. W niniejszym artykule odczytuję wybrane kroniki literackie komentujące dwa teksty opublikowane przez Gurian w Rumunii w latach 1945‑1946 – Zilele nu se întorc niciodată [Dni nigdy nie powracają] oraz Întâmplări între amurg și noapte [Zdarzenia między zmierzchem a nocą]. Kroniki te pokazują bowiem, w jaki sposób postrzegano Innego, w tym przypadku – pisarkę, niepełnosprawną kobietę czy Żydówkę w xx wieku. Ta perspektywa ma na celu wskazać uwarunkowania nie‑ estetyczne (płeć, cielesność, klasa społeczna, poglądy polityczne, pochodzenie etniczne itd.), które zdecydowały o pojawieniu i zniknięciu Gurian na scenie literackiej, a które ciągle określają postrzeganie jej tekstów w Rumunii. Na końcu tego studium zastanawiam się nad możliwością rehabilitacji tej postaci w historii literatury europejskiej, co mogłoby z kolei przyczynić się do odnowienia rumuńskiego kanonu literackiego xx wieku, w którym nadal nie ma miejsca dla pisarek. Cazul Soranei Gurian (1913‑1956) ilustrează situația unei excluderi din considerențe multiple în societatea europeană din secolul xx‑lea. Fiind femeie, evreică și străină, acuzată de spionaj și de colaborare, trupul său, cu handicap și atins de cancer, devine principalul vinovat al acestei exilări plurale. Autorea este un personaj tragic: nu numai din cauza vieții sale, ci și din cauza uitării în care a căzut opera sa, totuși originală și recunoscută de către contemporanii ei, compusă din șase volume în limba franceză și în română, precum și de zeci de publicații în presă. În acest articol, propun o lectură a unor cronici literare privind cele două ediții ale Soranei Gurian publicate în România în anii 1945‑1946 – Zilele nu se întorc niciodată și Aventuri între amurg și noapte. Aceste cronici reflectă modul în care se percepe Celălalt, în acest caz – o scriitoare, o femeie cu handicap, o evreică în contextul secolului xx. Această perspectivă are să identifice diferite condiționări (gen, corporalitate, clasă socială, convingeri politice, etnie șamd), care au determinat atît apariția, cît și dispariția lui Gurian de pe scenă literară și care încă înfluențează modul de percepere al textelor sale în România. La sfîrșitul acestui studiu, propun o reflecție asupra posibilității de reabilitare a acestei figuri în istoria literaturii europene, ceea ce ar putea conduce la rediscutarea canonului literar românesc al secolului xx, unde scriitoarele încă nu‑și găsesc locul.


2011 ◽  
Vol 20 (2) ◽  
Author(s):  
H. C. Stempels

AbstractAstronomy has been on the curriculum of Uppsala University from at least the middle of the 15th century. However, since Uppsala also was the ecclesiastical centre of Sweden, the acceptance of new ideas, such as the Copernican heliocentric system, was slow. At the same time, more peripheral universities in the Swedish empire, including Dorpat/Tartu, enjoyed a larger freedom. It was not until the early 18th century that a ‘modern’ astronomy emerged in Uppsala. This effort was to a large extent led by Anders Celsius (1701-1744), who was able to establish good international contacts with astronomers in continental Europe. Celsius participated in De Maupertuis’ expedition to the far north of Sweden, in order to measure the meridian arc and determine the shape of the Earth. This paper explores how Celsius became involved in De Maupertuis’ expedition, and how this effort paved the way to the establishment of a fully equipped astronomical observatory, including an extensive collection of books and instruments, most of which survives up to this day.


2021 ◽  
Author(s):  
Rafael Ferber

This book provides an introduction to six key concepts within philosophy: philosophy itself, language, knowledge, truth, being and the good. At the same time, it aims to initiate its readers into the processes of philosophical thinking. The book is addressed to students and lay persons, but also contains new ideas for specialists. It is written in a clear, accessible and engaging style. The German version appeared in eight editions and the second revised and updated English editon has the potential to become a key textbook for an international audience.


2018 ◽  
Vol 28 (06) ◽  
pp. 1049-1090 ◽  
Author(s):  
Nithi Rungtanapirom

We construct a torsion-free arithmetic lattice in [Formula: see text] arising from a quaternion algebra over [Formula: see text]. It is the fundamental group of a square complex with universal covering [Formula: see text], a product of trees with constant valency [Formula: see text], which has minimal Euler characteristic. Furthermore, our lattice gives rise to a fake quadric over [Formula: see text] by means of non-archimedean uniformization.


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