This page is intended as place for newer texts related with "Combinatorial group theory". Older texts in this area are

Papers on knots (1983-1984). See the page Meridional generators, ….
The first proof of the bijectivity of the norm residue homomorphism mod 2 in degree 3 used the Reidemeister-Schreier method for subgroup presentations. See On Hilbert Satz 90 for K₃ for degree-two extensions (May 1986).
On a cubic identity for involutive Hopf algebras (July 2022)

Generators and relations for the symmetric group

by Markus Rost (Notes, August 2026, 5 pages)

We derive the well-known Coxeter-type presentation of the symmetric group.

Full text (August 7, 2026): [pdf]

On permutation braids

by Markus Rost (Notes, August 2026, 10 pages)

We construct the "permutation braid" section from the symmetric group to the braid group in terms of generators and relations.

The text is at a preliminary stage, but the main construction is presented with all details.

Full text (August 7, 2026): [pdf]