Part 6: A new algebra structure on compositions (quasi-symmetric functions), distinct from the QSym algebra.
Back to Part 5.
On to Part 7.
Back to research page.
The multiplication we define here is analogous to the product in MSym.
In fact, drawing the compositions as "combs of combs" with the lower comb's nodes colored,
we at first multipy exactly as in MSym.
The rule is that
if the leftmost leaf is split, then all coloring is removed above the graft;
whereas if the leftmost leaf is not split,
then all nodes below the graft are colored.
Finally, the passage to compositions is achieved by "combing,"
where the colored nodes are transformed into a single comb.