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Refers to citizens of the small city Hamtramck, in MI. It is usually used in a negative tone meaning that the certain Hamtramck citizen is rude, dirty, disgusting and overall beneath you.
"Ugh. Hamtramck is full of Hamtrash."

"Someone needs to send some garbage men to Hamtramck to clean out the Hamtrash"
by krisitup December 12, 2012