Combinatorics of normal sequence of positive generalized braids

I give here some results on combinatorics of normal sequence of positive generalized braids of exceptionnal type introduced in
A divisibility result in combinatorics of generalized braids with L. Foissy, in J of Comb. Theory Serie A, vol. 152, 190-224 (2017) arXiv

Type $\text{F}_4$

Adjacency matrix : F4-adj-matrix.txt.
Characteristic polynomial : F4-characteristic.txt.
Generating series : F4-gen-series.txt.
Numbers : F4-numbers.txt.

Type $\text{H}_3$

Adjacency matrix : H3-adj-matrix.txt.
Characteristic polynomial : H3-characteristic.txt.
Generating series : H3-gen-series.txt.
Numbers : H3-numbers.txt.

Type $\text{H}_4$

Adjacency matrix : H4-adj-matrix.txt.
Characteristic polynomial : H4-characteristic.txt.
Generating series : H4-gen-series.txt.
Numbers : H4-numbers.txt.

Type $\text{E}_6$

Adjacency matrix : E6-adj-matrix.txt.
Characteristic polynomial : E6-characteristic.txt.
Generating series : E6-gen-series.txt.
Numbers : E6-numbers.txt.

Type $\text{E}_7$

Adjacency matrix : E7-adj-matrix.txt.
Characteristic polynomial : E7-characteristic.txt.
Generating series : E7-gen-series.txt.
Numbers : E7-numbers.txt.