Brown Dwarf Binaries

Nearly 500 brown dwarfs have been discovered in recent years. The majority of these brown dwarfs exist in the solar neighborhood, yet determining their fundamental properties (mass, age, temperature & metallicity) has proved to be quite difficult, with current estimates relying heavily on theoretical models. Binary brown dwarfs provide a unique opportunity to empirically determine fundamental properties, which can then be used to test model predictions. In addition, the observed binary fractions, separations, mass ratios, & orbital eccentricities can provide insight into the formation mechanism of these low-mass objects. I will review the results of various brown dwarf multiplicity studies, and will discuss what we have learned about the formation and evolution of brown dwarfs by examining their binary properties as a function of age and mass.

Comparing skew Schur functions: a quasisymmetric perspective

Reiner, Shaw and van Willigenburg showed that if two skew Schur functions sA and sB are equal, then the skew shapes $A$ and $B$ must have the same "row overlap partitions." Here we show that these row overlap equalities are also implied by a much weaker condition than Schur equality: that sA and sB have the same support when expanded in the fundamental quasisymmetric basis F. Surprisingly, there is significant evidence supporting a conjecture that the converse is also true. In fact, we work in terms of inequalities, showing that if the F-support of sA contains that of sB, then the row overlap partitions of A are dominated by those of B, and again conjecture that the converse also holds. Our evidence in favor of these conjectures includes their consistency with a complete determination of all F-support containment relations for F-multiplicity-free skew Schur functions. We conclude with a consideration of how some other quasisymmetric bases fit into our framework.