Combinatorial Hopf Algebras I: The Hopf Algebra YSym of Binary TreesLast time we looked at the definition of Hopf algebras, using the group algebra as a motivating example. This time I want to look at YSym, a Hopf algebra of binary trees. This is an example of a Combinatorial Hopf Algebra (CHA), meaning a Hopf algebra defined over some combinatorial object such as partitions, compositions, permutations, trees. The binary trees we're concerned with are the familiar
