threw 120 pitches in his fourth complete game of the year.

"It was on me that the slide lasted as long as it did. I wanted to change the tide today...we have five more games at home and I'm sure my teammates will step up."

Hayato Sakamoto doubled in the opening run off Nao Higashihama (6-2) in the third. Seiji Kobayashi plated another in the fourth with a single despite a superb play by Hawks center fielder Yuki Yanagita, who fired a bullet to the plate only to see the umpire let the run stand after replays.

In the seventh, Sugano reached on a single before scoring the Giants' third run on Sakamoto's base hit. A wild pitch and Casey McGehee's double added two more runs in the frame before Suganocurrently pursuing his Ph.D. in combinatorics at Rutgers University under the supervision of Doron Zeilberger. His wife Kristen is also pursuing her Ph.D. at Rutgers in Classical Studies.

Ron Umble is a professor of mathematics at Millersville University of Pennsylvania, where he has been a faculty member since 1984. His research interests are in algebraic topology and the theory of generalized operads, in particular. He has directed numerous undergraduate research projects and has coauthered three published papers with students (including this one). He is a member of the Pennsylvania Zeta chapter (Temple University) of Pi Mu Epsilon and was the 1972 winner of the Zeta chapter’s student paper competition.

[^1]: The results in this paper appeared in the first author’s undergraduate thesis supervised by the second author.
