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Triangulations of polygons and stacked simplicial complexes: separating their Stanley–Reisner ideals
A triangulation of a polygon has an associated Stanley–Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals and...
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Gröbner Bases of Determinantal Ideals
Chapter 4 presents the computation of Gröbner bases, based on standard bitableaux and the Robinson-Schensted-Knuth correspondence to which it gives a...
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An Extension of Gröbner Basis Theory to Indexed Polynomials Without Eliminations
In computer algebra, it remains to be challenging to establish general computational theories for determining the equivalence of indexed polynomials....
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Resolutions of letterplace ideals of posets
We investigate resolutions of letterplace ideals of posets. We develop topological results to compute their multigraded Betti numbers, and to give...
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Ideals Associated to Poset Homomorphisms: A Survey
In this survey, we give an overview to the various known algebraic properties and invariants of ideals of poset homomorphisms. A particular attention...
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Algebraic properties of ideals of poset homomorphisms
Given finite posets P and Q , we consider a specific ideal L ( P , Q ), whose minimal monomial generators correspond to order-preserving maps
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A Symbolic Approach to Generation and Analysis of Finite Difference Schemes of Partial Differential Equations
We discuss three symbolic approaches for the generation of a finite difference scheme of a general single partial differential equation (PDE). We...
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Tensor representations of the general linear super group
We show a correspondence between tensor representations of the super general linear group GL(m|n) and tensor representations of the general linear...
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The Method of Virtual Variables and Representations of Lie Superalgebras
We provide a brief account of Capelli’s method of virtual variables and of its relations with representations of general linear Lie superalgebras....
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The work of Gian-Carlo rota on invariant theory
The purpose of this paper is twofold: first, to explain Gian-Carlo Rota’s work on invariant theory; second, to place this work in a broad historical...
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A formal theory of resultants (I): an algorithm in invariant theory
Let A = a < b < … be an infinite alphabet of negative letters, and let P = u 1 < u 2 < ⋯ < u...
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Grassmann geometric calculus, invariant theory and superalgebras
The idea of exploring and develo** the deep connections between the theory of Cayley-Grassmann algebras and the invariant theory of skew-symmetric...
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Classification of Trivectors in 6-D Space
We give a characteristic-free classification of the invariants and co-variants of skew symmetric tensors of step three in six-dimensional space...