Lattice Diagram polynomials in one set of variables

The space $M_{\mu/i,j}$ spanned by all partial derivatives of the lattice polynomial $\Delta_{\mu/i,j}(X;Y)$ is investigated in math.CO/9809126 and many conjectures are given. Here, we prove all these conjectures for the $Y$-free component $M_{\mu/i,j}^0$ of $M_{\mu/i,j}$. In particular, we give an explicit bases for $M_{\mu/i,j}^0$ which allow us to prove directly the central {\sl four term recurrence} for these spaces.Comment: 15 page

A Critical Examination of Halo White Dwarf Candidates

A detailed analysis of halo white dwarf candidates is presented, which is based on model atmosphere fits to observed energy distributions built from photoelectric or photographic magnitudes. Most of the candidates identified in reduced proper motion diagrams are shown to be too warm (Teff > 5000 K) and most likely too young to be members of the galactic halo, while the tangential velocities of the cooler and thus older white dwarfs are shown to be entirely consistent with the disk population. The results suggest that some white dwarf stars born in the young disk may have high velocities with respect to the local standard of rest. Such objects could represent the remnants of donor stars from close mass-transfer binaries that produced type Ia supernovae via the single degenerate channel, or other scenarios suggested in the literature. Ongoing surveys that rely solely on reduced proper motion diagrams are likely to identify more of these high velocity young degenerates, rather than to unveil the old white dwarf population of the galactic halo. The importance of infrared photometry for studying extremely cool white dwarfs is also emphasized.Comment: Accepted for publication in the Astrophysical Journal, 16 pages, 9 figure

Mitosis recursion for coefficients of Schubert polynomials

Mitosis is a rule introduced by [Knutson-Miller, 2002] for manipulating subsets of the n by n grid. It provides an algorithm that lists the reduced pipe dreams (also known as rc-graphs) [Fomin-Kirillov, Bergeron-Billey] for a permutation w in S_n by downward induction on weak Bruhat order, thereby generating the coefficients of Schubert polynomials [Lascoux-Schutzenberger] inductively. This note provides a short and purely combinatorial proof of these properties of mitosis.Comment: 9 pages, to appear in JCT

President Bergeron\u27s 98th Commencement Address

President Bergeron offers remarks on A Whole New Way of Listening to the Class of 2016