We compute the limit distribution for the (centered and scaled) length of the longest increasing subsequence of random colored permutations. The limit distribution function is a power of that for usual random permutations computed recently by Baik, Deift, and Johansson (math.CO/9810105). In the two–colored case our method provides a different proof of a similar result by Tracy and Widom about t...

Connections between longest increasing subsequences in random permutations and eigenvalues of random matrices with complex entries have been intensely studied. This note applies properties of random elements of the finite general linear group to obtain results about the longest increasing subsequence in non-uniform random permutations.

Introduction: Previous investigations have shown that, with few exceptions, the lunar surface consists of a regolith layer that completely covers the underlying bedrock. The average thickness of this regolith layer has been estimated to be about 4-5 m for the mare and about 10-15 m for the highlands [1]. Knowledge of the structure, composition and distribution of the lunar regolith provides imp...

Using B, R and Hα images of roughly equal-sized samples of low surface brightness (LSB) and high surface brightness (HSB) galaxies (∼40 galaxies apiece), we have explored the dependence of H II region properties on local and global disc surface brightness. We have done this by constructing co-added H II region luminosity functions (LFs) according to local and central disc surface brightness and...

The gas mass fraction of spiral galaxies is strongly correlated with the central surface brightness of their disks. There exist many dim galaxies with long gas consumption time scales and fg > 0.5. This resolves the gas consumption paradox. The surface density of gas follows the optical surface brightness, but does not vary by as large a factor. This is the signature of a critical density thres...

Abrupt changes in luminance trigger and restrict brightness filling-in. If brightness was actively filled-in and mediated by cells signaling both luminance borders and surface brightness, then brightness spreading could also get disrupted by changes in texture. We measured psychophysically the brightness of a uniform luminance disk, which was segmented into two parts by different textures. The ...