in gulliver's part1
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The two parties in Lilliput are Tramecksan and Slamecksan; they are distinguished by the high and low heels of their shoes.
The people of Lilliput and Blefuscu are unable to get along because years ago, after an emperor's son was injured trying to break his egg on the smaller end (the traditional way of egg breaking), he decreed that no one may break the smaller end of his egg. This caused a great uproar among many of the Lilliputians and led to six rebellions and thousands of deaths. Eventually the Big-Endians were exiled and went to Blefuscu, where they gained favor and convinced the government to go to war against Lilliput.
The Big-Endians were those who broke their eggs on the "big" end. Sorry, I read more into your question than you asked. It doesn't get much simpler than this!