We obtain a presentation of a certain orientation preserving periodic homeomorphism of a compact real surface of genus by a product of right handed Dehn twists using a splitting family. It was expected that a presentation of a homeomorphism by right handed Dehn twists obtained from a splitting family is one of the shortest presentation. In this paper, we give a counter example of this conjecture.
"One parameter families of Riemann surfaces and presentations of elements of mapping class group by Dehn twists." J. Math. Soc. Japan 58 (2) 585 - 594, April, 2006. https://doi.org/10.2969/jmsj/1149166790