 
Summary: Journal of Combinatorial Theory, Series A 91, 5 14 (2000)
On a Problem in Shuffling
Noga Alon1
Tel Aviv University, Tel Aviv, Israel
and
Ken Berman2
and Daniel Kleitman2
Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA 02139
Communicated by the Managing Editors
Received March 10, 2000
dedicated to the memory of giancarlo rota
Upper and lower bounds are obtained for the number of shuffles necessary to
reach the ``furthest'' two hand deal starting from a given permutation of a deck of
cards. The bounds are on the order of (log2 n)Ā2 and log log n, respectively.
2000 Academic Press
1. INTRODUCTION
Suppose we take a deck of n cards, shuffle it in the usual way k times,
and then deal the cards all out, again in the usual way, giving nĀj cards to
each of j hands. We consider the following question: suppose we always
start with a fresh deck, with cards in a fixed order; how large must k be,
