Séminaire Lotharingien de Combinatoire, 89B.32 (2023), 12 pp.
Nantel Bergeron, Kelvin Chan, Farhad Soltani and
Mike Zabrocki
Quasisymmetric Harmonics of the Exterior Algebra
Abstract.
We study fermionic quasisymmetric polynomials in the polynomial ring Rn with n anticommuting variables. The main results of this paper are that the quasisymmetric polynomials in Rn form a commutative sub-algebra of Rn, there is a basis of the quotient of Rn by the ideal In generated by the
quasisymmetric polynomials in Rn that is indexed by ballot sequences, and there is a basis of the ideal generated by quasisymmetric polynomials
that is indexed by sequences that break the ballot condition.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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