Part 6: A new algebra structure on compositions (quasi-symmetric functions), distinct from the QSym algebra.

The multiplication. Back to Part 5. On to Part 7. Back to research page.

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.

Back to Part 5. On to Part 7. Back to research page.

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