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pro vyhledávání: '"05E05"'
We study a variety of questions centered around the computation of cohomology of line bundles on the incidence correspondence (the partial flag variety parametrizing pairs consisting of a point in projective space and a hyperplane containing it). Ove
Externí odkaz:
http://arxiv.org/abs/2411.13450
This paper investigates methods for calculating the chromatic symmetric function (CSF) of a graph in chromatic-bases and the $m_\lambda$-basis. Our key contributions include a novel approach for calculating the CSF in chromatic-bases constructed from
Externí odkaz:
http://arxiv.org/abs/2411.13411
The fundamental quasisymmetric functions in superspace are a generalization of the fundamental quasisymmetric functions involving anticommuting variables. We obtain the action of the product, coproduct, and antipode on the fundamental quasisymmetric
Externí odkaz:
http://arxiv.org/abs/2411.13371
We show how to use Clifford algebra techniques to describe the de Rham cohomology ring of equal rank compact symmetric spaces $G/K$. In particular, for $G/K=U(n)/U(k)\times U(n-k)$, we obtain a new way of multiplying Schur polynomials, i.e., computin
Externí odkaz:
http://arxiv.org/abs/2411.11663
Autor:
Kling, Filip Jonsson, Lundqvist, Samuel, Mohammadi, Fatemeh, Orth, Matthias, Sáenz-de-Cabezón, Eduardo
For the almost complete intersection ideals $(x_1^2, \dots, x_n^2, (x_1 + \cdots + x_n)^k)$, we compute their reduced Gr\"obner basis for any term ordering, revealing a combinatorial structure linked to lattice paths, elementary symmetric polynomials
Externí odkaz:
http://arxiv.org/abs/2411.10209
Autor:
Cape, Noah, Zemel, Shaul
The fact that Schubert polynomials are the weighted counting functions for reduced RC-graphs, also known as reduced pipe dreams, was established using their generating functions inside an appropriate Demazure algebra. Here we investigate the generati
Externí odkaz:
http://arxiv.org/abs/2411.08465
We give a counting formula in terms of modified Hall-Littlewood polynomials and the chromatic quasisymmetric function for the number of points on an arbitrary Hessenberg variety over a finite field. As a consequence, we express the Poincar\'e polynom
Externí odkaz:
http://arxiv.org/abs/2411.05096
We show that all totally positive formal power series with integer coefficients and constant term $1$ are precisely the rank-generating functions of Schur-positive upho posets, thereby resolving the main conjecture proposed by Gao, Guo, Seetharaman,
Externí odkaz:
http://arxiv.org/abs/2411.04123
The celebrated Cauchy identity expresses the product of terms $(1 - x_i y_j)^{-1}$ for $(i,j)$ indexing entries of a rectangular $m\times n$-matrix as a sum over partitions $\lambda$ of products of Schur polynomials: $s_{\lambda}(x)s_{\lambda}(y)$. A
Externí odkaz:
http://arxiv.org/abs/2411.03117
Autor:
Tom, Foster, Vailaya, Aarush
We describe a way to decompose the chromatic symmetric function as a positive sum of smaller pieces. We show that these pieces are $e$-positive for cycles. Then we prove that attaching a cycle to a graph preserves the $e$-positivity of these pieces.
Externí odkaz:
http://arxiv.org/abs/2410.21762