5. Combinatorics

Tree hook length formulas can be specified via a Hopf algebra.

• A Unifying Approach for Proving Hook-Length Formulas for Weighted Tree Families, Graphs and Combinatorics, 29 no. 6, (2013) p 1839–1865.

• Tree hook length formulae, Feynman rules and B-series, Annales de l’Institut Henri Poincaré D, 2 no. 4 (2015), p. 413–430. arXiv:1412.6053.

Though I admit hook length formulas are not that interesting and may already fit under Hazewinkel's description of 5. Also the first paper doesn't actually use Hopf algebras and the second alludes to them.