Remarkable Rainbow Phenomena

Remarkable cardinals

To a large extent, the scientific work of both Peter Koepke and Philip Welch has always been inspired by Ronald Jensen’s fine structure theory and his Covering Lemma for L, the constructible universe. Cf., e.g., their joint papers [5] and [6]. In this paper we aim to play with the theme that large cardinals compatible with “V=L,” specifically: remarkable cardinals, allow us to create situations...

Rainbow Matchings and Rainbow Connectedness

Aharoni and Berger conjectured that every collection of n matchings of size n+1 in a bipartite graph contains a rainbow matching of size n. This conjecture is related to several old conjectures of Ryser, Brualdi, and Stein about transversals in Latin squares. There have been many recent partial results about the Aharoni-Berger Conjecture. The conjecture is known to hold when the matchings are m...

Rainbow.

Remarkable Asymmetric Random Walks

There exists an asymmetric probability measure P on the real line with P n (]0; 1)+ (1=2)P n (f0g) = 1=2 for every n 2 N. P can be chosen absolutely continuous and P can be chosen to be concentrated on the integers. In both cases, P can be chosen to have moments of every order, but P can not be determined by its moments. 1 Questions and results Let P be a probability measure on the real line R,...

Technology Critique: ReMarkable Texts

ReMarkable Texts (RMT) is an “electronic student notebook” currently under development by Brown Computer Science Department's Computer Graphics Group. Running on a TabletPC, the system aims to replace and augment the standard paper notebook with an electronic device. RMT offers a variety of tools for manipulating and annotating documents, including simple note-taking with the Tablet's stylus, s...