Authorities say Alexander Wang was stopped at the building's entrance just after 6:30 p.m.
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Secret Service agents reportedly found the large knife and a Swiss Army knife in his bag. He also allegedly had handcuffs, a water pistol and fireworks.
Police say a search of his dorm room uncovered additional fireworks, and charges are pending.
Wang told detectives he is a business student who likes to study at Trump Tower, and that he has been at Trump Tower at least 10 times since Election Day.
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When asked why he had all the gear in his bag, he claimed to be a survivalist and that he meant to harm no one.
Officials say there is no link to terror or a militia, but Wang's actions prompted further investigation.
The building has attracted leaders from across the nation as the transition effort continues to unfold. In fact, former Texas Governor Rick Perry walked through the lobby just minutes before Wang was arrested.
The ATF website carries an illustration of the firecracker Wang allegedly had in his possession, described as an M-100.