Number of orbits of Discrete Interval Exchanges

A new recursive function on discrete interval exchange transformation associated to a composition of length $r$, and the permutation $\sigma(i) = r -i +1$ is defined. Acting on composition $c$, this recursive function counts the number of orbits of the discrete interval exchange transformation associated to the composition $c$. Moreover, minimal discrete interval exchanges transformation i.e. the ones having only one orbit, are reduced to the composition which label the root of the Raney tree. Therefore, we describe a generalization of the Raney tree using our recursive function

Open heavy-flavour measurements in pp and Pb-Pb collisions with ALICE at the LHC

We present an overview of measurements related to open heavy-flavour production with the ALICE experiment at the LHC. Studies are performed using single leptons (electrons at mid-rapidity and muons at forward-rapidity) and D mesons, which are reconstructed via their hadronic decay channels. The measured differential production cross sections in proton-proton collisions at $\sqrt{s}$ = 2.76 and 7 TeV are in agreement with perturbative QCD calculations. Results from Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV on the nuclear modification factor $R_{AA}$ are shown, along with the elliptic flow $\nu_2$

The Tragedy of a Cambridge Feminist

Overview: Stephen Frug sits down at his computer desk on April 4th, 2011. His wife, Sarah, is in the kitchen trying to feed their three year old son and for once, all is quiet. He picks up his glasses and slides them on his face, then continues to log onto his online blog. He had started writing the blog in 2005 when he was still a 34 year old graduate student in the history department of Cornell University. Since then, he’d gotten his Ph.D. and started teaching history at Hobart and William Smith in Geneva, New York, an hour\u27s drive away from his home in Ithaca. Stephen reminisces as he clicks through some of his older blog posts. He smiles as he scrolls past the post about his son’s birthday and another about the frustrations he had while trying to write his graphic novel. A few minutes later, he finds himself staring at a new, blank entry. He had, after all, logged onto this blog for a particular reason. Taking a big sigh, he finally begins to write. “Twenty years ago today my mother, Mary Joe Frug, was murdered about a block from our house in Cambridge, Massachusetts. It was early evening; she was out for a walk. No one was ever caught or charged; we have no idea, to this day, who killed her. It was less than a month after my twentieth birthday.” Author\u27s Reflection: My name is Ellen Lapointe and I am currently a nursing major at St. John Fisher College. As my classes progress I am realizing that I love nursing and cannot wait to work in a hospital one day, but I also have a true passion for writing. Writing this paper, at least to me, was much different than any other paper I’ve written previously. Having a whole class centered on one final paper really made me very conscious about research as well as the editing process. It was also a different experience because I was writing about something that I was truly interested in, and I felt like a detective as I pried deeper into the lives of the victim and all of the people involved in the case. At first I stumbled upon some road blocks that put a temporary halt to my writing. As I tried to look up more information surrounding this 1991 murder mystery, I was having trouble finding information. With the help of the librarians, my professor, and some of my peers, I was able to find more clues that helped me write my paper. Although I put a lot of time and energy into writing and editing this paper, I now look back on it and I am genuinely proud of the effort I made, even if it’s not perfect

Heavy-flavour decay lepton measurements in pp, p-Pb, and Pb-Pb collisions with ALICE at the LHC

We present the measurements of electrons and muons from the semi-leptonic decays of heavy-flavour hadrons measured in the central and forward rapidity regions with ALICE in pp, Pb-Pb, and p-Pb, collisions at the LHC. The pT-differential production cross section in pp collisions, the elliptic flow in Pb-Pb collisions, and the nuclear modification factor in Pb-Pb and p-Pb collisions are shown. The results are compared to theoretical predictions.Comment: 8 pages, 6 figures, International Conference on the Initial Stages in High-Energy Nuclear Collisions (IS2013

Jack polynomials in superspace

This work initiates the study of {\it orthogonal} symmetric polynomials in superspace. Here we present two approaches leading to a family of orthogonal polynomials in superspace that generalize the Jack polynomials. The first approach relies on previous work by the authors in which eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland Hamiltonian were constructed. Orthogonal eigenfunctions are now obtained by diagonalizing the first nontrivial element of a bosonic tower of commuting conserved charges not containing this Hamiltonian. Quite remarkably, the expansion coefficients of these orthogonal eigenfunctions in the supermonomial basis are stable with respect to the number of variables. The second and more direct approach amounts to symmetrize products of non-symmetric Jack polynomials with monomials in the fermionic variables. This time, the orthogonality is inherited from the orthogonality of the non-symmetric Jack polynomials, and the value of the norm is given explicitly.Comment: 28 pages. Corrected version of lemme 3 and other minor corrections and 2 new references; version to appear in Commun. Math. Phy

The Murnaghan-Nakayama rule for k-Schur functions

We prove the Murgnaghan--Nakayama rule for $k$-Schur functions of Lapointe and Morse, that is, we give an explicit formula for the expansion of the product of a power sum symmetric function and a $k$-Schur function in terms of $k$-Schur functions. This is proved using the noncommutative $k$-Schur functions in terms of the nilCoxeter algebra introduced by Lam and the affine analogue of noncommutative symmetric functions of Fomin and Greene.Comment: 23 pages, updated to reflect referee comments, to appear in Journal of Combinatorial Theory, Series

From Jack to Double Jack Polynomials via the Supersymmetric Bridge

The Calogero-Sutherland model occurs in a large number of physical contexts, either directly or via its eigenfunctions, the Jack polynomials. The supersymmetric counterpart of this model, although much less ubiquitous, has an equally rich structure. In particular, its eigenfunctions, the Jack superpolynomials, appear to share the very same remarkable combinatorial and structural properties as their non-supersymmetric version. These super-functions are parametrized by superpartitions with fixed bosonic and fermionic degrees. Now, a truly amazing feature pops out when the fermionic degree is sufficiently large: the Jack superpolynomials stabilize and factorize. Their stability is with respect to their expansion in terms of an elementary basis where, in the stable sector, the expansion coefficients become independent of the fermionic degree. Their factorization is seen when the fermionic variables are stripped off in a suitable way which results in a product of two ordinary Jack polynomials (somewhat modified by plethystic transformations), dubbed the double Jack polynomials. Here, in addition to spelling out these results, which were first obtained in the context of Macdonal superpolynomials, we provide a heuristic derivation of the Jack superpolynomial case by performing simple manipulations on the supersymmetric eigen-operators, rendering them independent of the number of particles and of the fermionic degree. In addition, we work out the expression of the Hamiltonian which characterizes the double Jacks. This Hamiltonian, which defines a new integrable system, involves not only the expected Calogero-Sutherland pieces but also combinations of the generators of an underlying affine ${\widehat{\mathfrak {sl}}_2}$ algebra