One of the ingredients in a paper that Bram Petri and I submitted in 2016 was a count of integer matrices of determinant 1 with non-negative entries and bounded trace.
Our paper only required an upper bound, but as a number theorist I couldn’t resist the temptation of describing the asymptotics of this function more precisely. In this post we explore do just that, exploring Dirchlet’s hyperbola method along the way.
In this post, we’ll look at one-player games of limited information (sometimes classified as puzzles, not games) through a topological lens, and create for each game a poset of topologies under which topologically indistinguishable points correspond to outcomes that are indiscernible in a limited-information context. Expanding this dictionary, we’ll describe a topology on the outcome space under which the “safe” or “warranted” extension of one’s limited information relates to the continuity of certain maps.
a. w. walker 