In How Many Ways Can You Play Stanley Solitaire?
By Shalosh B. Ekhad and Doron Zeilberger
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.tex
Written: June 23, 2024
Dedicated to Richard Stanley (b. June 23, 1944) a non-bossy superboss, on his 80th birthday.
We introduce a very simple solitaire game, easily explained to a smart five-year-old, for which an
explicit closed-form formula for the number of ways of playing it can be explained to a smart
seven-year-old, but, alas, whose proof can be only understood by a very smart (and motivated)
24-year-old graduate student in algebraic combinatorics. It is inspired by the seminal work of
Richard Stanley from 1984.
Maple package
-
StanleySolitaire.txt,
a Maple package to investigate the Solitaire game described in the paper. In particular it conjectures expressions for initial configurations in Stanley Solitaire.
Sample Input and Output for StanleySolitaire.txt
If you want to see Explicit expressions for the number of ways of playing Stanley Solitaire with initial position
[b,0k,a] where a ≥ b and 0 ≤ k ≤ 15
then input gives the
output.
If you want to see Explicit expressions for the number of ways of playing Stanley Solitaire with initial position
[a,0k,a-j] where a > j, 0 ≤ j ≤ 10 and j+1 ≤ k ≤ j+10,
then input gives the
output.
If you want to see Explicit expressions for the number of ways of playing Stanley Solitaire with initial position
[a2,a3,a1]
where a1 ≥ a2 ≥ a3 ≥ 1, and an interesting implication for the number of reduced decompositions of the assoicated permutation
then input gives the
output.
Doron Zeilberger's Home Page