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This volume marks the 20th anniversary of the New York Number Theory Seminar (NYNTS). Beginning in 1982, the NYNTS has tried to present a broad spectrum of research in number theory and related fields of mathematics, from physics to geometry to combinatorics and computer science. The list of seminar speakers includes not only Fields Medallists and other established researchers, but also many other...
A geometric progression of length k and integer ratio is a set of numbers of the form for some positive real number a and integer r ≥ 2. For each integer k ≥ 3, a greedy algorithm is used to construct a strictly decreasing sequence $(a_i)_{i=1}^{∞}$ of positive real numbers with a₁ = 1 such that the set $G^{(k)} = ⋃ _{i=1}^{∞} (a_{2i}, a_{2i-1}]$ contains...
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