Zobrazeno 1 - 10
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pro vyhledávání: '"Khare, Apoorva"'
Autor:
Damase, Sujit Sakharam, Khare, Apoorva
We show that a normed linear space is isometrically isomorphic to an inner product space if and only if it is a strongly $n$-point homogeneous metric space for any (or every) $n \geqslant 3$. The counterpart for $n=2$ is the Banach-Mazur problem.
Externí odkaz:
http://arxiv.org/abs/2312.08106
Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent adv
Externí odkaz:
http://arxiv.org/abs/2310.18041
We continue the study of real polynomials acting entrywise on matrices of fixed dimension to preserve positive semidefiniteness, together with the related analysis of order properties of Schur polynomials. Previous work has shown that, given a real p
Externí odkaz:
http://arxiv.org/abs/2310.18020
Graham showed with Pollak and Hoffman-Hosoya that for any directed graph $G$ with strong blocks $G_e$, the determinant $\det(D_G)$ and cofactor-sum $cof(D_G)$ of the distance matrix $D_G$ can be computed from the same quantities for the blocks $G_e$.
Externí odkaz:
http://arxiv.org/abs/2309.08691
Autor:
Khare, Apoorva
Recently, a general version of the Hoffmann-Jorgensen inequality was shown jointly with Rajaratnam [Ann. Probab. 2017], which (a) improved the result even for real-valued variables, but also (b) simultaneously unified and extended several versions in
Externí odkaz:
http://arxiv.org/abs/2307.03125
Autor:
Khare, Apoorva, Tikaradze, Akaki
Publikováno v:
Journal of Algebraic Combinatorics 58 (2023), no. 3, 761-773
Motivated by recent results of Tao-Ziegler [Discrete Anal. 2016] and Greenfeld-Tao (2022 preprint) on concatenating affine-linear functions along subgroups of an abelian group, we show three results on recovering affine-linearity of functions $f : V
Externí odkaz:
http://arxiv.org/abs/2212.02429
A weight-formula for all highest weight modules, and a higher order parabolic category $\mathcal{O}$
Autor:
Khare, Apoorva, Teja, G. Krishna
Let $\mathfrak{g}$ be a complex Kac-Moody algebra, with Cartan subalgebra $\mathfrak{h}$. Also fix a weight $\lambda\in\mathfrak{h}^*$. For $M(\lambda)\twoheadrightarrow V$ an arbitrary highest weight $\mathfrak{g}$-module, we provide a cancellation-
Externí odkaz:
http://arxiv.org/abs/2203.05515
Publikováno v:
Seminaire Lotharingien de Combinatoire 86B (2022), Article #42
For every finite simple connected graph $G = (V,E)$, we introduce an invariant, its blowup-polynomial $p_G(\{ n_v : v \in V \})$. This is obtained by dividing the determinant of the distance matrix of its blowup graph $G[{\bf n}]$ (containing $n_v$ c
Externí odkaz:
http://arxiv.org/abs/2203.04105
Autor:
Khare, Apoorva, Sahi, Siddhartha
Publikováno v:
European Journal of Combinatorics 110 (2023), art. # 103683, 16 pp
Cauchy's determinant formula (1841) involving $\det ((1-u_i v_j)^{-1})$ is a fundamental result in symmetric function theory. It has been extended in several directions, including a determinantal extension by Frobenius [J. reine angew. Math. 1882] in
Externí odkaz:
http://arxiv.org/abs/2201.03129