query: field_of_work anatoly vershik
supports: A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br>
  It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. In mathematics, the notion of permutation relates to the act of arranging all the members of a set into some sequence or order, or if the set is already ordered, rearranging (reordering) its elements, a process called permuting. These differ from combinations, which are selections of some members of a set where order is disregarded. For example, written as tuples, there are six permutations of the set {1,2,3}, namely: (1,2,3), (1,3,2), (2,1,3), (2,3,1), (3,1,2), and (3,2,1). These are all the possible orderings of this three element set. As another example, an anagram of a word, all of whose letters are different, is a permutation of its letters. In this example, the letters are already ordered in the original word and the anagram is a reordering of the letters. The study of permutations of finite sets is a topic in the field of combinatorics. Mathematics (from Greek  "máthma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. Anatoly Moiseevich Vershik ( Russian :    ; born on 28 December 1933 in Leningrad ) is a Soviet and Russian mathematician . He is most famous for his joint work with Sergey V. Kerov on representations of infinite symmetric groups and applications to the longest increasing subsequences . Vershik studied at Leningrad State University , receiving his doctoral degree in 1974 ; his advisor was Vladimir Rokhlin . He works at the Steklov Institute of Mathematics and at Saint Petersburg State University . In 1998 -- 2008 he was the president of the St. Petersburg Mathematical Society . In 2012 he became a fellow of the American Mathematical Society . His doctoral students include Alexander Barvinok , Anna Erschler and Sergey Fomin . In abstract algebra, the symmetric group S on a finite set of "n" symbols is the group whose elements are all the permutation operations that can be performed on "n" distinct symbols, and whose group operation is the composition of such permutation operations, which are defined as bijective functions from the set of symbols to itself. Since there are "n"! ("n" factorial) possible permutation operations that can be performed on a tuple composed of "n" symbols, it follows that the order (the number of elements) of the symmetric group S is "n"!.
candidates: combinatorics computing mathematician mathematics
answer: combinatorics