Results 11 to 20 of about 393 (215)
On Determinantal Varieties of Hankel Matrices [PDF]
Algebra, 2014 Let ℌ be a class of n×n Hankel matrices HA whose entries, depending on a given matrix A, are linear forms in n variables with coefficients in a finite field 𝔽q. For every matrix in ℌ, it is shown that the varieties specified by the leading minors of orders from 1 to n-1 have the same number qn-1 of points in 𝔽qn.
Edoardo Ballico, Michele Elia
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Jacobi–Trudi formulas and determinantal varieties [PDF]
Algebraic Combinatorics, 2023 Gessel gave a determinantal expression for certain sums of Schur functions which visually looks like the classical Jacobi–Trudi formula. We explain the commonality of these formulas using a construction of Zelevinsky involving BGG complexes and use this explanation to generalize this formula in a few different directions.
Sam, Steven V, Weyman, Jerzy
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The Representation Type of Determinantal Varieties [PDF]
Algebras and Representation Theory, 2017 This is a postprint (AAM) of an article published in Algebras and Representation Theory.
Kleppe, Jan O. +1 more
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Arcs on determinantal varieties [PDF]
Transactions of the American Mathematical Society, 2012 27 pages. This is part of the author's PhD thesis at the University of Illinois at Chicago. v2: Minor changes.
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On minimality of determinantal varieties [PDF]
Linear Algebra and its Applications, 2021 We prove that semialgebraic sets of rectangular matrices of a fixed rank, of skew-symmetric matrices of a fixed rank and of real symmetric matrices whose eigenvalues have prescribed multiplicities are minimal submanifolds of the space of real matrices of a given size.
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A geometric view of cryptographic equation solving
Journal of Mathematical Cryptology, 2008 This paper considers the geometric properties of the Relinearisation algorithm and of the XL algorithm used in cryptology for equation solving. We give a formal description of each algorithm in terms of projective geometry, making particular use of the ...
Murphy S., Paterson M. B.
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Schubert varieties, toric varieties and ladder determinantal varieties [PDF]
Annales de l'Institut Fourier, 1997 We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties.
Gonciulea, Nicolae +1 more
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Littlewood Complexes and Analogues of Determinantal Varieties [PDF]
International Mathematics Research Notices, 2014 31 pages; v2: added more details to proofs and calculations; v3: corrected typos and changed section/theorem ...
Sam, Steven V, Weyman, Jerzy
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Toric double determinantal varieties [PDF]
Communications in Algebra, 2021 Undergraduate ...
Alexander Blose +3 more
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Mixed Ladder Determinantal Varieties
Journal of Algebra, 2000 The authors generalize the notion of ladder determinantal varieties, which was introduced by Abhyankar, by allowing ideals of minors of different size of a matrix of indeterminates. Then they explore the relation between these mixed ladder determinantal varieties and Schubert varieties. Next they show that, up to product by affine spaces, each of these
Gonciulea, Nicolae, Miller, Claudia
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