Heinrich August Rothe

Heinrich August Rothe (1773 to 1842) was a German mathematician and professor of mathematics at Erlangen, a student of Carl Hindenburg and a member of Hindenburg's school of combinatorics. Born in Dresden, he became a docent at the University of Leipzig in 1793, an extraordinary professor there in 1796, and in 1804 a full professor at Erlangen. His 1793 thesis contained a summation formula for binomial coefficients now called the Rothe-Hagen identity, and in 1800 he was the first to define the inverse of a permutation. He introduced the square diagram now called the Rothe diagram and used it to show that a matrix and its transpose have the same determinant. He also studied involutions, found a recurrence that counts them, and in 1811 was the first to formulate the q-binomial theorem.