3 papers
math.CO2008
Jumping sequences
Steve Butler, Ron Graham, Nan Zang
An integer sequence a(n) is called a jump sequence if a(1)=1 and 1<=a(n)<n for n>=2. Such a sequence has the property that a^k(n)=a(a(...(a(n))...)) goes to 1 in finitely many step…
math.CO2008
Some Ramsey results for the n-cube
Ron Graham, Jozsef Solymosi
In this note we establish a Ramsey-type result for certain subsets of the -dimensional cube. This can then be applied to obtain reasonable bounds on various related structures,…
math.CO2008
Enumerating (multiplex) juggling sequences
Steve Butler, Ron Graham
We consider the problem of enumerating periodic -juggling sequences of length for multiplex juggling, where is the initial state (or {\em landing schedule}) of the balls…