arXiv subjects

Joseph DiMuro

Publications and source records attributed to Joseph DiMuro.

3 recordsLinked to original sources

arXiv2018

The Warden's de Bruijn Sequence

The Warden's Game is a 2-player game, played with a row of coins. One player (the prisoner) wants to get all coins to show tails; the other player (the warden) wants to delay that as long as possible. At each turn, one player transfers the coin on the far right to the far left, and optionally flips that coin; the prisoner transfers heads, and the warden transfers tails. We will find the optimal strategies for both players, and we will also analyze some variations on this game.

math.CO↗

arXiv2018

Classifying Rotationally-Closed Languages Having Greedy Universal Cycles

Let $\textbf{T}(n,k)$ be the set of strings of length $n$ over the alphabet $Σ=\{1,2,\ldots,k\}$. A universal cycle for $\textbf{T}(n,k)$ can be constructed using a greedy algorithm: start with the string $k^n$, and continually append the least symbol possible without repeating a substring of length $n$. This construction also creates universal cycles for some subsets $\textbf{S}\subseteq\textbf{T}(n,k)$; we will classify all such subsets that are closed under rotations.

math.CO↗

arXiv2015

On On_p

Generalizing John Conway's construction of the Field On_2, we give the "minimal" definitions of addition and multiplication that turn the ordinals into a Field of characteristic p, for any prime p. We then analyze the structure of the resulting Field, which we will call On_p.

math.RA↗