Related papers: A geometrization of Stanley--Reisner theory
We study the deformation theory of projective Stanley-Reisner schemes associated to combinatorial manifolds. We achieve detailed descriptions of first order deformations and obstruction spaces. Versal base spaces are given for certain…
The present work represents a step to deal with stellar structure using a pure geometric approach. A geometric field theory is used to construct a model for a spherically symmetric configuration. The model obtained can be considered as a…
In this paper we go on to discuss about Stanley's theorem in Integer partitions. We give two different versions for the proof of the generalization of Stanley's theorem illustrating different techniques that may be applied to profitably…
In this paper, a geometric interpretation is provided of a new rational Landen transformation. The convergence of its iterates is also established.
In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.
We show that the Stanley-Reisner ideal of the one-dimensional simplicial complex whose diagram is an $n$-gon is always a set-theoretic complete intersection in any positive characteristic.
In this paper, we give a geometrization and a generalization of a lemma of differential Galois theory. This geometrization, in addition of giving a nice insight on this result, offers us the occasion to investigate several points of…
We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.
For a simplicial complex $\Delta$, we introduce a simplicial complex attached to $\Delta$, called the expansion of $\Delta$, which is a natural generalization of the notion of expansion in graph theory. We are interested in knowing how the…
We give a purely combinatorial characterization of complete Stanley-Reisner rings having principally generated (equivalently, finitely generated) Cartier algebras.
These notes provide a survey of the theory of plane partitions, seen through the glasses of the work of Richard Stanley and his school.
A triangulation of a polygon has an associated Stanley-Reisner ideal. We obtain a full algebraic and combinatorial understanding of these ideals, and describe their separated models. More generally we do this for stacked simplicial…
We present a new geometric proof of Stanley's monotonicity theorem for lattice polytopes, using an interpretation of $\delta$-polynomials of lattice polytopes in terms of orbifold Chow rings.
In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.
The aim of this paper is to make a connection between design theory and algebraic geometry/commutative algebra. In particular, given any Steiner System $S(t,n,v)$ we associate two ideals, in a suitable polynomial ring, defining a Steiner…
We present the geometry and symmetries of radiative transfer theory. Our geometrization exploits recent work in the literature that enables to obtain the Hamiltonian formulation of radiative transfer as the semiclassical limit of a phase…
The letter provides a geometrical interpretation of frequency in electric circuits. According to this interpretation, the frequency is defined as a multivector with symmetric and antisymmetric components. The conventional definition of…
We reconstruct Karl Friston's active inference and give a geometrical interpretation of it.
Feynman diagram expressions in ordinary field theories can be written in a string-like manner. The methods and the advantages for doing so are briefly discussed.
We expose a rather simple and direct approach to the structure theory of prime PI-rings ("Posner's theorem"), based on fundamental properties of the extended centroid of a prime ring.