In How Ways Can You Play Stanley Solitaire?

By Shalosh B. Ekhad and Doron Zeilberger


.pdf    .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 ispired by the seminal work of Richard Stanley from 1984.


Maple package


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