Resources for "Multi-headed lattices and Green functions"

This webpage contains Mathematica resources for the paper "Multi-headed lattices and Green functions" (J. Phys. A 57 (2024), no. 46, Paper No. 465204. arXiv:2405.20294) by Qipin Chen, Shane Chern and Lin Jiu.

You may find the Mathematica notebooks and PDF screenshots (in case you have no access to Mathematica) for the results in this paper. Since some computations for telescopers take too much time, we include these telescopers in separate files if you do not want to execute such exhausting computations.

Heracles lattices (Sect. 4)

4D (Sect. 4.3)

Theorem 4.2: Differential equation
Theorem 4.3: Recurrence

Creative telescoping for the integral expression:
『Notebook』 『PDF』 『Telescopers』

Creative telescoping for the summation expression:
『Notebook』 『PDF』 『Telescopers』

Pólya number:
『Notebook』 『PDF』

5D (Sect. 4.4)

Theorem 4.6: Differential equation
Theorem 4.7: Recurrence

Creative telescoping for the summation expression:
『Notebook』 『PDF』
『Telescopers: Even-indexed and Odd-indexed subsequences』

Pólya number:
『Notebook』 『PDF』

Cerberus lattices (Sect. 5)

5D (Sect. 5.1)

Theorem 5.1: Differential equation
Theorem 5.2: Recurrence

Creative telescoping for the integral expression:
『Notebook』 『PDF』
『Annihilators (Telescopers + Certificates):
　Second integral, Third integral, Fourth integral, Fifth integral』

Initial values of $\tilde{r}_{3,5}$ ($n=0,\ldots,55$):
『TXT』

Pólya number:
『Notebook』 『PDF』

Minimal recurrences (Sect. 6)

4D Orthrus lattice (Theorem 6.1)

Theorem 6.1: Recurrence

『Notebook』 『PDF』

5D Orthrus lattice (Theorem 6.2)

Theorem 6.2: Recurrence

『Notebook』 『PDF』

Crystal structure of NaCl (Fig. 1)

『Notebook』 『PDF』