Polynomiality of monotone Hurwitz numbers in higher genera

Hurwitz numbers count branched covers of the Riemann sphere with specified ramification, or equivalently, transitive permutation factorizations in the symmetric group with specified cycle types. Monotone Hurwitz numbers count a restricted subset of these branched covers, related to the expansion of complete symmetric functions in the Jucys-Murphy elements, and have arisen in recent work on the the asymptotic expansion of the Harish-Chandra-Itzykson-Zuber integral. In previous work we gave an explicit formula for monotone Hurwitz numbers in genus zero. In this paper we consider monotone Hurwitz numbers in higher genera, and prove a number of results that are reminiscent of those for classical Hurwitz numbers. These include an explicit formula for monotone Hurwitz numbers in genus one, and an explicit form for the generating function in arbitrary positive genus. From the form of the generating function we are able to prove that monotone Hurwitz numbers exhibit a polynomiality that is reminiscent of that for the classical Hurwitz numbers, i.e., up to a specified combinatorial factor, the monotone Hurwitz number in genus g with ramification specified by a given partition is a polynomial indexed by g in the parts of the partition.Comment: 23 page

Toda Equations and Piecewise Polynomiality for Mixed Double Hurwitz Numbers

This article introduces mixed double Hurwitz numbers, which interpolate combinatorially between the classical double Hurwitz numbers studied by Okounkov and the monotone double Hurwitz numbers introduced recently by Goulden, Guay-Paquet and Novak. Generalizing a result of Okounkov, we prove that a certain generating series for the mixed double Hurwitz numbers solves the 2-Toda hierarchy of partial differential equations. We also prove that the mixed double Hurwitz numbers are piecewise polynomial, thereby generalizing a result of Goulden, Jackson and Vakil

Equilibrium composition between liquid and clathrate reservoirs on Titan

Hundreds of lakes and a few seas of liquid hydrocarbons have been observed by the Cassini spacecraft to cover the polar regions of Titan. A significant fraction of these lakes or seas could possibly be interconnected with subsurface liquid reservoirs of alkanes. In this paper, we investigate the interplay that would happen between a reservoir of liquid hydrocarbons located in Titan's subsurface and a hypothetical clathrate reservoir that progressively forms if the liquid mixture diffuses throughout a preexisting porous icy layer. To do so, we use a statistical-thermodynamic model in order to compute the composition of the clathrate reservoir that forms as a result of the progressive entrapping of the liquid mixture. This study shows that clathrate formation strongly fractionates the molecules between the liquid and the solid phases. Depending on whether the structure I or structure II clathrate forms, the present model predicts that the liquid reservoirs would be mainly composed of either propane or ethane, respectively. The other molecules present in the liquid are trapped in clathrates. Any river or lake emanating from subsurface liquid reservoirs that significantly interacted with clathrate reservoirs should present such composition. On the other hand, lakes and rivers sourced by precipitation should contain higher fractions of methane and nitrogen, as well as minor traces of argon and carbon monoxide.Comment: Accepted for publication in Icaru

La tenue des assises seigneuriales dans les campagnes angevines (fin XIVe-milieu XVIe siècles)

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« Corps outragés, chairs meurtries ». Images, perceptions, enjeux de la violence corporelle à la lumière de sources judiciaires (Anjou-Maine, XIVe-XVIe siècles)

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Le procès d’un couple d’empoisonneurs en Anjou à la fin du Moyen Âge

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Jean de Bourdigné

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Justice royale, justice ducale et justices seigneuriales en Anjou et dans le Maine au temps du roi René

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Les justices seigneuriales en Anjou et dans le Maine à la fin du Moyen Âge

Résumé éditeur : Fondée sur le dépouillement exhaustif d’archives de la pratique judiciaire, cette étude tente une approche à la fois quantitative et qualitative des registres audienciers d’affaires judiciaires et d’amendes, tout en faisant une large place au droit coutumier en vigueur en Anjou et dans le Maine. Cette recherche examine ainsi la manière dont l’audience s’organise, le personnel qu’elle mobilise, mais également l’activité quotidienne des tribunaux seigneuriaux à travers la procédure suivie, le type d’affaires jugées et les condamnations prononcées. Elle dégage les « modèles » susceptibles d’avoir influencé la conduite de l’exercice judiciaire dans cette région et à ce niveau institutionnel