Triangle-Free Triangulations, Hyperplane Arrangements and Shifted Tableaux

Flips of diagonals in colored triangle-free triangulations of a convex polygon are interpreted as moves between two adjacent chambers in a certain graphic hyperplane arrangement. Properties of geodesics in the associated flip graph are deduced. In particular, it is shown that: (1) every diagonal is flipped exactly once in a geodesic between distinguished pairs of antipodes; (2) the number of geodesics between these antipodes is equal to twice the number of Young tableaux of a truncated shifted staircase shape.Comment: figure added, plus several minor change

The Diabetic Dog as a Translational Model for Human Islet Transplantation.

The dog model has served as the primary method for early development of many diabetes therapies, including pancreatic islet transplantation techniques and immunosuppressive protocols. Recent trends towards the use of monoclonal antibody therapies for immunosuppression in human islet transplantation have led to the increasing use of primate models with induced diabetes. In addition to induced-disease models in large animals, scientists in many fields are considering the use of naturally-occurring disease models in client-owned pets. This article will review the applicability of naturally-occurring diabetes in dogs as a translational model for developing islet transplantation in the human diabetic patient

Flag weak order on wreath products

A generating set for the wreath product \ZZ_r \wr S_n which leads to a nicely behaved weak order is presented, and properties of the resulting order are studied.Comment: 20 pages, 2 figures; corrected and added proofs and explanation

Do Not Speak about Love. Speak about Compassion.

First, let me say one or two things about the word love. Love is such a used, abused, and misused word that people should possibly stay away from it. We use it for all kinds of purposes, to contain all kinds of meanings. Most of them are completely disconnected and unimportant. The word is especially abused in the English language, where you have love and divine love and "whatever" love. You have also the phrase making love, which is not exactly like love, but at least has a veiy clear-cut meaning. We should use other words for this, in order not be confused and mistaken. Today, we will look at the concept of love in international affairs and love in the university. The very combinations seem somehow impossible, or perhaps too ugly, to contemplate. Having discussed the problems with the word love, let me say a few words about how I would define it. I am not going to try to make a comprehensive definition—it's too complex and too hard. But to make a definition that has a clear meaning, clear enough to comprehend in itself, and to set borders and limits, let us say that— in essence—love is the basic experience of a feeling for the Other. In its simplest form, it is the motion of going out from myself toward the Other. That is the essence of love, and therefore any other meaning you give the word is marring it, obscuring it or making fraudulent claims

On Degrees in the Hasse Diagram of the Strong Bruhat Order

For a permutation $\pi$ in the symmetric group $S_n$ let the {\it total degree} be its valency in the Hasse diagram of the strong Bruhat order on $S_n$, and let the {\it down degree} be the number of permutations which are covered by $\pi$ in the strong Bruhat order. The maxima of the total degree and the down degree and their values at a random permutation are computed. Proofs involve variants of a classical theorem of Tur\'an from extremal graph theory.Comment: 14 pages, minor corrections; to appear in S\'em. Lothar. Combi