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 $\nu_2$

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

Order ideals in weak subposets of Young's lattice and associated unimodality conjectures

The k-Young lattice Y^k is a weak subposet of the Young lattice containing partitions whose first part is bounded by an integer k>0. The Y^k poset was introduced in connection with generalized Schur functions and later shown to be isomorphic to the weak order on the quotient of the affine symmetric group by a maximal parabolic subgroup. We prove a number of properties for $Y^k$ including that the covering relation is preserved when elements are translated by rectangular partitions with hook-length $k$. We highlight the order ideal generated by an $m\times n$ rectangular shape. This order ideal, L^k(m,n), reduces to L(m,n) for large k, and we prove it is isomorphic to the induced subposet of L(m,n) whose vertex set is restricted to elements with no more than k-m+1 parts smaller than m. We provide explicit formulas for the number of elements and the rank-generating function of L^k(m,n). We conclude with unimodality conjectures involving q-binomial coefficients and discuss how implications connect to recent work on sieved q-binomial coefficients.Comment: 18 pages, 5 figure

Review of nondiffracting Bessel beams

The theory of nondiffracting beam propagation and experimental evidence for nearly-nondiffractive Bessel beam propagation are reviewed. The experimental results are reinterpreted using simple optics formulas, which show that the observed propagation distances are characteristic of the optical systems used to generate the beams and do not depend upon the initial beam profiles. A set of simple experiments are described which support this interpretation. It is concluded that nondiffracting Bessel beam propagation has not yet been experimentally demonstrated