field_of_work anatoly vershik
Anatoly Moiseevich Vershik ( Russian :          ; born on 28 December 1933 in Leningrad ) is a Soviet and Russian ___MASK42___ . 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 ___MASK63___ 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 . ___MASK63___ ( 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 ___MASK63___ . In ___MASK63___ , 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 ___MASK49___ . A ___MASK42___ is someone who uses an extensive knowledge of ___MASK63___ in his / her work , typically to solve mathematical problems . 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 "!. A mathematical problem is a problem that is amenable to being represented , analyzed , and possibly solved , with the methods of ___MASK63___ . 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 ___MASK43___ , such as Hilbert ' s problems .< br > It can also be a problem referring to the ___MASK43___ of ___MASK63___ itself , such as Russell ' s Paradox .