Ž. Ž We study the structure of hypersurface orbital varieties of sl N, ‫ރ‬ those that . are hypersurfaces in the nilradical of some parabolic subalgebra and how information about this structure is encoded in the standard Young tableau associated to it by the Robinson᎐Schensted algorithm. We present a conjecture for the exact form of the unique non-linear defining equations of hypersurface orbital varieties and proofs of the conjecture in certain cases.

No abstract

Abstract. We show that the specialization of nonsymmetric Macdonald polynomials at t = 0 are, up to multiplication by a simple factor, characters of Demazure modules for sl(n). This connection furnishes Lie-theoretic proofs of the nonnegativity and monotonicity of Kostka polynomials.

Color charts, or grids of evenly spaced multicolored dots or squares, appear in the work of modern artists and designers. Often the artist ⁄ designer distributes the many colors in a way that could be described as ''random,'' that is, without an obvious pattern. We conduct a statistical analysis of 125 ''random-looking'' art and design color charts and show that they differ significantly from truly random color charts in the average distance between adjacent colors. We argue that this attribute generalizes results in subjective randomness in a black ⁄ white setting and gives further evidence supporting a connection between subjective randomness and what is esthetically pleasing.

We study common tendencies adult hiders have in choosing and changing positions in the game of hide-and-seek. In our case, the game takes the form of commercial and homemade advent calendars in which the creator has hidden Numbers 1, 2, . . ., 24 in a seemingly random way. By comparing the numberings in the 332 human-generated calendars with random numberings, we identify common tendencies that hiders share. We observe that hiders hide things far apart and spread out from each other, the behavior which is consistent with, but concurrently extends previous research on hiding and its connection with subjective randomness.