Her research concerned combinatorics: she was a pioneer in the study of permutation patterns, and an expert on noncrossing partitions.
[4] Simion's thesis research concerned the concavity and unimodality of certain combinatorially defined sequences,[5] and included what Richard P. Stanley calls "a very influential result" that the zeros of certain polynomials are all real.
[8] Simion also did extensive research on noncrossing partitions, and became "perhaps the world's leading authority" on them.
[2][9] She was also a leader in George Washington University's annual Summer Program for Women in Mathematics.
[2] As well as being a mathematician, Simion was a poet and painter;[6][10] her poem "Immigrant Complex" was published in a collection of mathematical poetry in 1979.