Ideals and quotients of diagonally quasi-symmetric functions
The electronic journal of combinatorics, Tome 24 (2017) no. 3
In 2004, J.-C. Aval, F. Bergeron and N. Bergeron studied the algebra of diagonally quasi-symmetric functions $\operatorname{\mathsf{DQSym}}$ in the ring $\mathbb{Q}[\mathbf{x},\mathbf{y}]$ with two sets of variables. They made conjectures on the structure of the quotient $\mathbb{Q}[\mathbf{x},\mathbf{y}]/\langle\operatorname{\mathsf{DQSym}}^+\rangle$, which is a quasi-symmetric analogue of the diagonal harmonic polynomials. In this paper, we construct a Hilbert basis for this quotient when there are infinitely many variables i.e. $\mathbf{x}=x_1,x_2,\dots$ and $\mathbf{y}=y_1,y_2,\dots$. Then we apply this construction to the case where there are finitely many variables, and compute the second column of its Hilbert matrix.
DOI :
10.37236/6658
Classification :
05E05, 13P10
Mots-clés : quasi-symmetric functions, Gröbner bases
Mots-clés : quasi-symmetric functions, Gröbner bases
Affiliations des auteurs :
Shu Xiao Li 1
@article{10_37236_6658,
author = {Shu Xiao Li},
title = {Ideals and quotients of diagonally quasi-symmetric functions},
journal = {The electronic journal of combinatorics},
year = {2017},
volume = {24},
number = {3},
doi = {10.37236/6658},
zbl = {1367.05206},
url = {http://geodesic.mathdoc.fr/articles/10.37236/6658/}
}
Shu Xiao Li. Ideals and quotients of diagonally quasi-symmetric functions. The electronic journal of combinatorics, Tome 24 (2017) no. 3. doi: 10.37236/6658
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