Gröbner-Shirshov basis for the finitely presented algebras defined by permutation relations of symmetric type
Qiu, Jianjun · Chen, Yuqun
Original · EN
In this paper, we give a Gröbner-Shirshov basis for the finitely presented semigroup algebra k[Sₙ(Symₙ)] defined by permutation relations of symmetric type. As an application, by the Composition-Diamond Lemma, we obtain normal forms of elements of momoid Sₙ(Symₙ), which gives an answer to an open problem posted by F. Cedó, E. Jespers and J. Okniński [7] for the symmetric group case.
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