Japanese poetry the "honored guest" composing a few beginning lines, often in the form of the "hokku" (which, as a stand-alone piece, eventually evolved into the haiku). This initial sally was followed by a stanza composed by the "host." This process could continue, sometimes with many stanzas composed by numerous other "guests", until the final conclusion. Other collaborative forms of Japanese poetry also evolved, such as the "renku" ("linked-verse") form. In other cases, the poetry collaborations were more competitive, such as with "uta-awase" gatherings, in which Heian period poets composed "waka" poems on set themes, with a judge deciding the winner(s). Haiku
Invariant of a binary form for the ring of covariants. showed that the ring of invariants of a degree 8 form is generated by 9 invariants of degrees 2, 3, 4, 5, 6, 7, 8, 9, 10, and the ring of covariants is generated by 69 covariants. August von Gall () and confirmed the generators for the ring of invariants and showed that the ideal of relations between them is generated by elements of degrees 16, 17, 18, 19, 20. showed that the algebra of invariants of a degree 9 form is generated by 92 invariants. Cröni, Hagedorn, and Brouwer computed 476 covariants, and Lercier