Catalan's intervals and realizers of triangulations

The Stanley lattice, Tamari lattice and Kreweras lattice are three remarkable orders defined on the set of Catalan objects of a given size. These lattices are ordered by inclusion: the Stanley lattice is an extension of the Tamari lattice which is an extension of the Kreweras lattice. The Stanley order can be defined on the set of Dyck paths of size $n$ as the relation of \emph{being above}. Hence, intervals in the Stanley lattice are pairs of non-crossing Dyck paths. In a former article, the second author defined a bijection $\Phi$ between pairs of non-crossing Dyck paths and the realizers of triangulations (or Schnyder woods). We give a simpler description of the bijection $\Phi$. Then, we study the restriction of $\Phi$ to Tamari's and Kreweras' intervals. We prove that $\Phi$ induces a bijection between Tamari intervals and minimal realizers. This gives a bijection between Tamari intervals and triangulations. We also prove that $\Phi$ induces a bijection between Kreweras intervals and the (unique) realizers of stack triangulations. Thus, $\Phi$ induces a bijection between Kreweras intervals and stack triangulations which are known to be in bijection with ternary trees.Comment: 22 page

Convergence rates for density estimators of weakly dependent time series

Assuming that $(X_t)_{t\in\Z}$ is a vector valued time series with a common marginal distribution admitting a density $f$, our aim is to provide a wide range of consistent estimators of $f$. We consider different methods of estimation of the density as kernel, projection or wavelets ones. Various cases of weakly dependent series are investigated including the Doukhan & Louhichi (1999)'s $\eta$-weak dependence condition, and the $\tilde \phi$-dependence of Dedecker & Prieur (2005). We thus obtain results for Markov chains, dynamical systems, bilinear models, non causal Moving Average... From a moment inequality of Doukhan & Louhichi (1999), we provide convergence rates of the term of error for the estimation with the \L^q loss or almost surely, uniformly on compact subsets

S-Packing Colorings of Cubic Graphs

Given a non-decreasing sequence $S=(s\_1,s\_2, \ldots, s\_k)$ of positive integers, an {\em $S$-packing coloring} of a graph $G$ is a mapping $c$ from $V(G)$ to $\{s\_1,s\_2, \ldots, s\_k\}$ such that any two vertices with color $s\_i$ are at mutual distance greater than $s\_i$, $1\le i\le k$. This paper studies $S$-packing colorings of (sub)cubic graphs. We prove that subcubic graphs are $(1,2,2,2,2,2,2)$-packing colorable and $(1,1,2,2,3)$-packing colorable. For subdivisions of subcubic graphs we derive sharper bounds, and we provide an example of a cubic graph of order $38$ which is not $(1,2,\ldots,12)$-packing colorable

Contribution of studies of sub-seismic fracture populations to paleo-hydrological reconstructions (Bighorn Basin, USA)

This work reports on the reconstruction of the paleo-hydrological history of the Bighorn Basin (Wyoming, USA) and illustrates the advantages and drawbacks of using sub-seismic diffuse fracture populations (i.e., micrometric to metric joints and veins forming heterogeneous networks), rather than fault zones, to characterize paleo-fluid systems at both fold and basin scales. Because sub-seismic fractures reliably record the successive steps of deformation of folded rocks, the analysis of the geochemical signatures of fluids that precipitated in these fractures reveals the paleo-fluid history not only during, but also before and after, folding. The present study also points out the need for considering pre-existing fluid systems and basin-scale fluid migrations to reliably constrain the evolution of fluid systems in individual folds

Validity of the one-dimensional limp model for porous materials

A straightforward criterion to determine the limp model validity for porous materials is addressed here. The limp model is an "equivalent fluid" model which gives a better description of the porous behavior than the well known "rigid frame" model. It is derived from the poroelastic Biot model assuming that the frame has no bulk stiffness. A criterion is proposed to identify the porous materials for which the limp model can be used. It relies on a new parameter, the Frame Stiffness Influence FSI based on porous material properties. The critical values of FSI under which the limp model can be used, are determined using a 1D analytical modeling for a specific boundary set: radiation of a vibrating plate covered by a porous layer.Comment: 12th International Student Conference on Electrical Engineering, Prague : Tch\`eque, R\'epublique (2008

Is the Collective Model of Labor Supply Useful for Tax Policy Analysis? A Simulation Exercise

The literature on household behavior contains hardly any empirical research on the within-household distributional effect of tax-benefit policies. We simulate this effect in the framework of a collective model of labor supply when shifting from a joint to an individual taxation system in France. We show that the net-of-tax relative earning potential of the wife is a significant determinant of intrahousehold negotiation but with very low elasticity. Consequently, the labor supply responses to the reform are entirely driven by the traditional substitution and income effects as in a unitary model. For some households only, the reform alters the intrahousehold distribution in a way that tends to change normative conclusions. A sensitivity analysis shows that the collective model would be required if the tax reform was both radical and of extended scope.Collective Model, Intrahousehold Allocation, Household Labor Supply, Tax Reform