ABSTRACT


FIBONACCI SOLITAIRE
Alexander Gnedin, Oktober 17, 2001
A deck of n cards with values 1,2,...,n is taken. The deck is shuffled, cards are turned up one at a time and dealt into or removed from a row on the table. Each time a card, say A, is turned we compare it with the lowest card on the table (if any), say B, and the cards are moved according to the rules:

(S): If A < B, then A is added to the row in the leftmost position, (C): If A > B, then both cards are removed.

(A is also dealt into the row when at the moment there are no other cards on the table.)

We argue that the chance to finish the game with no cards on the table is equal to the return probability for the standard random walk.

More generally, we discuss large-n asymptotics for the output configuration viewed as (i) a set, (ii) an involution, (iii) a lattice path or (iv) an interacting particle system.


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Martijn Pistorius (pistorius@math.uu.nl)

Last Updated: October 12, 2001