Some linear recurrences and their combinatorial interpretation by means of regular languages

AbstractIn this paper we apply ECO method and the concept of numeration systems to give a combinatorial interpretation to linear recurrences of the kind an=kan−1+han−2, where k>|h|⩾0. In particular, we define a language L such that the words of L having length n satisfy the recurrence, and then we describe a recursive construction for this language, according to the ECO method, and the corresponding finite succession rule

First-Digit Law in Nonextensive Statistics

Nonextensive statistics, characterized by a nonextensive parameter $q$, is a promising and practically useful generalization of the Boltzmann statistics to describe power-law behaviors from physical and social observations. We here explore the unevenness of the first digit distribution of nonextensive statistics analytically and numerically. We find that the first-digit distribution follows Benford's law and fluctuates slightly in a periodical manner with respect to the logarithm of the temperature. The fluctuation decreases when $q$ increases, and the result converges to Benford's law exactly as $q$ approaches 2. The relevant regularities between nonextensive statistics and Benford's law are also presented and discussed.Comment: 11 pages, 3 figures, published in Phys. Rev.

Exact Solution of the Discrete (1+1)-dimensional RSOS Model with Field and Surface Interactions

We present the solution of a linear Restricted Solid--on--Solid (RSOS) model in a field. Aside from the origins of this model in the context of describing the phase boundary in a magnet, interest also comes from more recent work on the steady state of non-equilibrium models of molecular motors. While similar to a previously solved (non-restricted) SOS model in its physical behaviour, mathematically the solution is more complex. Involving basic hypergeometric functions ${}_3\phi_2$, it introduces a new form of solution to the lexicon of directed lattice path generating functions.Comment: 10 pages, 2 figure

Degenerate flag varieties: moment graphs and Schr\"oder numbers

We study geometric and combinatorial properties of the degenerate flag varieties of type A. These varieties are acted upon by the automorphism group of a certain representation of a type A quiver, containing a maximal torus T. Using the group action, we describe the moment graphs, encoding the zero- and one-dimensional T-orbits. We also study the smooth and singular loci of the degenerate flag varieties. We show that the Euler characteristic of the smooth locus is equal to the large Schr\"oder number and the Poincar\'e polynomial is given by a natural statistics counting the number of diagonal steps in a Schr\"oder path. As an application we obtain a new combinatorial description of the large and small Schr\"oder numbers and their q-analogues.Comment: 25 page

Parking functions, labeled trees and DCJ sorting scenarios

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure

ISPY – NaCo imaging survey for planets around young stars : a young companion candidate embedded in the R CrA cloud

Context Within the NaCo-ISPY exoplanet imaging program, we aim at detecting and characterizing the population of low-mass companions at wide separations (≳10 AU), focusing in particular on young stars either hosting a known protoplanetary disk or a debris disk. Aims R CrA is one of the youngest (1-3 Myr) and most promising objects in our sample because of two previous studies that suggested the presence of a close companion. Our aim is to directly image and characterize the companion for the first time. Methods We observed R CrA twice with the NaCo instrument at the Very Large Telescope (VLT) in the L' filter with a one year time baseline in between. The high-contrast imaging data were reduced and analyzed and the companion candidate was detected in both datasets. We used artificial negative signals to determine the position and brightness of the companion and the related uncertainties. Results The companion is detected at a separation of 196.8 ± 4.5/196.6 ± 5.9 mas (18.7 ± 1.3/18.7 ± 1.4 AU) and position angle of 134.7 ± 0.5 ° /133.7 ± 0.7° in the first/second epoch observation. We measure a contrast of 7.29 ± 0.18/6.70 ± 0.15 mag with respect to the primary. A study of the stellar proper motion rejects the hypothesis that the signal is a background object. The companion candidate orbits in the clockwise direction and, if on a face-on circular orbit, its period is ˜43 - 47 yr. This value disagrees with the estimated orbital motion and therefore a face-on circular orbit may be excluded. Depending on the assumed age, extinction, and brightness of the primary, the stellar companion has a mass between 0.10 ± 0.02 M⊙ and 1.03-0.18+0.20 M⊙ range, if no contribution from circumsecondary material is taken into account. Conclusions As already hypothesized by previous studies, we directly detected a low-mass stellar companion orbiting the young Herbig Ae/Be star R CrA. Depending on the age assumptions, the companion is among the youngest forming companions imaged to date, and its presence needs to be taken into account when analyzing the complex circumstellar environment of R CrA

Encouraging female entrepreneurship in Jordan: environmental factors, obstacles and challenges

The number of female entrepreneurs and their contribution to the economy is steadily rising. Yet research suggests that female entrepreneurs face more challenges and barriers than their male counterparts. This is expected to be even more prevalent in Islamic contexts, which are characterised by conservative and patriarchal societies. In this research, 254 female business students from a private and a public university responded to a questionnaire that gauges their perceptions about potential barriers to entrepreneurship in Jordan and whether the business education they are receiving helps to prepare them for future entrepreneurial activity. Our results help to form a basis on which a deeper understanding of the phenomena can be achieved through more in depth future research. Among the main environmental factors that worry potential female entrepreneurs are the weakness of Jordanian economy, lack of finance, fear of risk, gender inequality and inability to maintain a work and private life balance. Our results also show that students are really not aware of the opportunities available to them and are unable to make a proper assessment. We call on both universities and the Jordanian government to put more emphasis on practical entrepreneurial education and encouraging women to play a much more active role within the workforce