The complete generating function for Gessel walks is algebraic

Supplementary Material

This is a collection of files accompanying an article of Alin Bostan and Manuel Kauers containing a proof that the complete generating function for Gessel walks is algebraic. The article itself can be downloaded here: [ps.gz] [pdf]

Section 1

Maple Session [mpl]

Section 2

Maple Session [mpl]
Coefficients of F(t,x) mod t¹⁰¹ [mpl] [mma]
The minimal polynomial of F(t,x) [mpl] [mma]

Section 3.1

Coefficients of G(t,x,0) mod t¹⁰⁰¹ [mpl] [mma] (75Mb)
Guessed differential operator for G(t,x,0) [mpl] [mma]
The minimal polynomial of G(t,x,0) [mpl] [mma]
Coefficients of G(t,0,y) mod t¹⁰⁰¹ [mpl] [mma] (45Mb)
Guessed differential operator for G(t,0,y) [mpl] [mma]
The minimal polynomial of G(t,0,y) [mpl] [mma]
Coefficients of U(t,x) mod t¹⁰⁰¹ [mpl] [mma] (75Mb)
The minimal polynomial of U(t,x) [mpl] [mma]
Coefficients of V(t,x) mod t¹⁰⁰¹ [mpl] [mma] (45Mb)
The minimal polynomial of V(t,x) [mpl] [mma]

Section 3.2

Details on existence of U_cand(t,x) and V_cand(t,x) [ps] [pdf]
Differential operators annihilating U_cand(t,x) [mma]
Recurrence operators annihilating the coefficients of U_cand(t,x) [mma]
Transformation matrix for U_cand(t,x) [mma]
Witness operators for U_cand(t,x) [mma]
The polynomial Q(T,t,y) whose solution is the auxiliary series f(t,y) [mma]
Differential operators annihilating f(t,x) [mma]
Recurrence operators annihilating the coefficients of f(t,x) [mma]
First transformation matrix for f(t,x) [mma]
First set of witness operators for f(t,x) [mma] (10Mb)
Second transformation matrix for f(t,x) [mma]
Second set of witness operators for f(t,x) [mma] (18Mb)

Section 3.3

The minimal polynomial of (1+x)G₂(t,x) - G(t;0,0) and x X(t,x)/t-G₁(t,X(t,x)) [mpl] [mma]

Section 3.4

Radical expression for G(t,1,1) [mpl] [mma]
Minimal polynomial of G(t,1,1) [mpl] [mma]
Radical expression for G(t,1,0) [mpl] [mma]
Minimal polynomial of G(t,1,0) [mpl] [mma]
Radical expression for G(t,0,1) [mpl] [mma]
Minimal polynomial of G(t,0,1) [mpl] [mma]