2 citations · 3 across the 5 of their papers we have counts for
5 papers
Generalizations of the M&M Game
Snehesh Das, Steven J. Miller, Geremias Polanco +4
The MandM Game involves two players who begin with I1 and I2 MandM's. During each round, each player tosses a fair coin: if the coin lands heads, that player eats one MandM, and if…
Decomposition of Beatty and Complementary Sequences
Geremias Polanco
In this paper we express the difference of two complementary Beatty sequences, as the sum of two Beatty sequences closely related to them. In the process we introduce a new Algorit…
Relaxed Wythoff has All Beatty Solutions
Jon Kay, Geremias Polanco
We find conditions under which the P-positions of three subtraction games arise as pairs of complementary Beatty sequences. The first game is due to Fraenkel and the second is an e…
A variation on the theme of Nicomachus
Florian Luca, Geremías Polanco, Wadim Zudilin
We prove some conjectures of K. Stolarsky concerning the first and third moment of the Beatty sequences with the golden section and its square.
Continuous Distribution Arising From the Three Gaps Theorem
Geremías Polanco, Daniel Schultz, Alexandru Zaharescu
The well known Three Gap Theorem states that there are at most three gap sizes in the sequence of fractional parts . It is known that if one averages over α, the dis…