Asymmetry in the reconstructed deceleration parameter

We study the orientation dependence of the reconstructed deceleration parameter as a function of redshift. We use the Union 2 and Loss datasets, by using the well known preferred axis discussed in the literature, finding the best fit reconstructed deceleration parameter. We found that a low redshift transition of the reconstructed $q(z)$ is clearly absent in one direction and amazingly sharp in the opposite one. We discuss the possibility that such a behavior can be associated with large scale structures affecting the data.Comment: 9 pages, 12 figure

Ehrhart clutters: Regularity and Max-Flow Min-Cut

If C is a clutter with n vertices and q edges whose clutter matrix has column vectors V={v1,...,vq}, we call C an Ehrhart clutter if {(v1,1),...,(vq,1)} is a Hilbert basis. Letting A(P) be the Ehrhart ring of P=conv(V), we are able to show that if A is the clutter matrix of a uniform, unmixed MFMC clutter C, then C is an Ehrhart clutter and in this case we provide sharp bounds on the Castelnuovo-Mumford regularity of A(P). Motivated by the Conforti-Cornuejols conjecture on packing problems, we conjecture that if C is both ideal and the clique clutter of a perfect graph, then C has the MFMC property. We prove this conjecture for Meyniel graphs, by showing that the clique clutters of Meyniel graphs are Ehrhart clutters. In much the same spirit, we provide a simple proof of our conjecture when C is a uniform clique clutter of a perfect graph. We close with a generalization of Ehrhart clutters as it relates to total dual integrality.Comment: Electronic Journal of Combinatorics, to appea