The lichen flora of the Chagos Archipelago : including a comparison with other island and coastal tropical floras

The 1996 Chagos Expedition provided the first opportunity to study the archipelago’s lichen flora. Seventeen of the 55 islands were ecologically investigated, some in more detail than others, and lists and representative collections of lichens have been assembled for many of them. In all, 67 taxa have been recorded, 52 to specific level. Although the islands have a low biodiversity for cryptogamic plants, as would be expected in terms of their relatively young age, remoteness and small terrestrial surface areas, those taxa that are present are often found in abundance and play significant ecological roles. There is a good correlation between total lichen biodiversity and island size, despite the fact that Cocos nucifera is such an important substratum for cryptogamic plants and its presence on all islands studied provides a consistently high associated species count. Comparisons of lichen floras for ten island and coastal tropical areas show good correlations (based on the Sörensen Coefficient) within the Indian Ocean as would be expected, but poorer correlations exist within and between Pacific Ocean and neotropical floras. Ranked correlations between Chagos and other floras are in the sequence Maldives > Laing Island > Aldabra > Tuamotu > Pitcairn > N.Mariana & Belize > Guadeloupe > Cook. When coefficients are calculated using only the Physciaceae, different correlations and sequences are derived, but the affinities of the Indian Ocean islands remain strong. However, although the lichen flora of Chagos is characteristic for an Indian Ocean, it is dominated by pantropical species

New Rotation Periods in the Open Cluster NGC 1039 (M 34), and a Derivation of its Gyrochronology Age

Employing photometric rotation periods for solar-type stars in NGC 1039 [M 34], a young, nearby open cluster, we use its mass-dependent rotation period distribution to derive the cluster's age in a distance independent way, i.e., the so-called gyrochronology method. We present an analysis of 55 new rotation periods,using light curves derived from differential photometry, for solar type stars in M 34. We also exploit the results of a recently-completed, standardized, homogeneous BVIc CCD survey of the cluster in order to establish photometric cluster membership and assign B-V colours to each photometric variable. We describe a methodology for establishing the gyrochronology age for an ensemble of solar-type stars. Empirical relations between rotation period, photometric colour and stellar age (gyrochronology) are used to determine the age of M 34. Based on its position in a colour-period diagram, each M 34 member is designated as being either a solid-body rotator (interface or I-star), a differentially rotating star (convective or C-star) or an object which is in some transitory state in between the two (gap or g-star). Fitting the period and photometric colour of each I-sequence star in the cluster, we derive the cluster's mean gyrochronology age. 47/55 of the photometric variables lie along the loci of the cluster main sequence in V/B-V and V/V-I space. We are further able to confirm kinematic membership of the cluster for half of the periodic variables [21/55], employing results from an on-going radial velocity survey of the cluster. For each cluster member identified as an I-sequence object in the colour-period diagram, we derive its individual gyrochronology age, where the mean gyro age of M 34 is found to be 193 +/- 9 Myr, formally consistent (within the errors) with that derived using several distance-dependent, photometric isochrone methods (250 +/- 67 Myr).Comment: accepted for publication in Astronomy & Astrophysic

Combinatorial representation theory of Lie algebras. Richard Stanley's work and the way it was continued

Richard Stanley played a crucial role, through his work and his students, in the development of the relatively new area known as combinatorial representation theory. In the early stages, he has the merit to have pointed out to combinatorialists the potential that representation theory has for applications of combinatorial methods. Throughout his distinguished career, he wrote significant articles which touch upon various combinatorial aspects related to representation theory (of Lie algebras, the symmetric group, etc.). I describe some of Richard's contributions involving Lie algebras, as well as recent developments inspired by them (including some open problems), which attest the lasting impact of his work.Comment: 11 page

What is Schur positivity and how common is it?

This is a short note about Schur positivity. We introduce Schur polynomials and explain how they appear in the representation theory of the general linear group. We end with a new result of the author with F. Bergeron and V. Reiner that gives the probability that a homogeneous symmetric polynomial with positive coefficients is Schur positive.Comment: 6 page

The Color-Period Diagram and Stellar Rotational Evolution - New Rotation Period Measurements in the Open Cluster M34

We present results from a 5-month photometric survey for stellar rotation periods combined with a 4-year radial-velocity survey for membership and binarity in the 220Myr open cluster M34. We report surface rotation periods for 120 stars, 83 of which are late-type cluster members. A comparison to previous work serves to illustrate the importance of high cadence long baseline photometric observations and membership information. The new M34 periods are less biased against slow rotation and cleaned for non-members. The rotation periods of the cluster members span more than an order of magnitude from 0.5 day up to 11.5 days, and trace two distinct rotational sequences - fast (C) and moderate-to-slow (I) - in the color-period diagram. The sequences represent two different states in the rotational evolution of the late-type cluster members. We use the color-period diagrams for M34 and for younger and older clusters to estimate the timescale for the transition from the C to the I sequence and find ~<150Myr, ~150-300Myr, and ~300-600Myr for G, early-mid K, and late K dwarfs, respectively. The small number of stars in the gap between C and I suggest a quick transition. We estimate a lower limit on the maximum spin-down rate (dP/dt) during this transition to be ~0.06 days/Myr and ~0.08 days/Myr for early and late K dwarfs, respectively. We compare the I sequence rotation periods in M34 and the Hyades for G and K dwarfs and find that K dwarfs spin down slower than the Skumanich rate. We determine a gyrochronology age of 240Myr for M34. We measure the effect of cluster age uncertainties on the gyrochronology age for M34 and find the resulting error to be consistent with the error estimate for the technique. We use the M34 I sequence to redetermine the coefficients in the expression for rotational dependence on color used in gyrochronology (abridged).Comment: 47 pages (12pt, preprint), 14 figures, 2 tables, Accepted for publication in ApJ, format of RA coordinates in Table 2 corrected in latest versio