Listar MAT_Articles por autoría "9fec35d0-f0a7-4af5-b147-3323d0db158b"
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A formula for the conductor of a semimodule of a numerical semigroup with two generators
Springer (2021-03-30)We provide an expression for the conductor c(Δ) of a semimodule Δ of a numerical semigroup Γ with two generators in terms of the syzygy module of Δ and the generators of the semigroup. In particular, we deduce that the ... -
Basic actions to reduce dropout rates in distance learning
(2018-02)Today’s society, which is strongly based on knowledge and interaction with information, has a key component in technological innovation, a fundamental tool for the development of the current teaching methodologies. Nowadays, ... -
Duality and syzygies for semimodules over numerical semigroups
Springer Verlag (2015-02)Let Γ=⟨α,β⟩ be a numerical semigroup. In this article we consider the dual Δ∗ of a Γ-semimodule Δ; in particular we deduce a formula that expresses the minimal set of generators of Δ∗ in terms of the generators of Δ. As ...
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Eliahou number, Wilf function and concentration of a numerical semigroup
Taylor & Francis (2022-03-30)We give an estimate of the minimal positive value of the Wilf function of a numerical semigroup in terms of its concentration. We describe necessary conditions for a numerical semigroup to have a negative Eliahou number ...
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Fractional ideals and integration with respect to the generalised Euler characteristic
Springer (2015)Let bb be a fractional ideal of a one-dimensional Cohen–Macaulay local ring containing a perfect field. This paper is devoted to the study of the motivic Poincaré series defined by different filtrations associated with bb ...
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Hilbert regularity of Z-graded modules over polynomial rings
Rocky Mountain Mathematics Consortium (2017-06)Let M be a finitely generated Z-graded module over the standard graded polynomial ring R=K[X1,…,Xd] with K a field, and let HM(t)=QM(t)/(1−t)d be the Hilbert series of~M. We introduce the Hilbert regularity of~M as the ...
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Hilbert series of modules over positively graded polynomial rings
Elsevier (2016-08)In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article ...
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How to compute the Stanley depth of a module
American Mathematical Society (2017)In this paper we introduce an algorithm for computing the Stanleydepth of a finitely generated multigraded module M over the polynomialring K[X1,...,Xn]. As an application, we give an example of a module whoseStanley depth ...
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Lattice paths with given number of turns and semimodules over numerical semigroups
Springer US (2014-06)Let Γ =< α, ß> be a numerical semigroup. In this article we consider several relations between the so-called Γ -semimodules and lattice paths from (0, α) to (ß,0): we investigate isomorphism classes of Γ -semimodules as ...
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LCM Lattices and Stanley Depth: A First Computational Approach
Taylor & Francis (2015-10)Let K be a field, and let S D K [X1, . . . ,Xn] be the polynomial ring. Let / be a monomial ideal of S with up to 5 generators. In this paper, we present a computational experiment which allows us to prove that depthS ...
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Linear optics only allows every possible quantum operation for one photon or one port
Elsevier (2017)We study the evolution of the quantum state of n photons in m different modes when they go through a lossless linear optical system. We show that there are quantum evolution operators U that cannot be built with linear ...
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Method to determine which quantum operations can be realized with linear optics with a constructive implementation recipe
American Physical Society (2019)The evolution of quantum light through linear optical devices can be described by the scattering matrix S of the system. For linear optical systems with m possible modes, the evolution of n input photons is given by a ...
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Minimal plane valuations
American Mathematical Society (AMS) (2018-07)We consider the value u(v)=lim m->m-1 a(mL) , where a(mL) is the last value of the vanishing sequence of Hº(mL) along a divisorial or irrational valuation v centered at Op2,p ,L (respectively, P ) being a line ...
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Multiple photon effective Hamiltonians in linear quantum optical networks
Elsevier (2019)We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based ...
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Newton–Okounkov bodies of exceptional curve valuations
European Mathematical Society (2020-03-20)We prove that the Newton–Okounkov body associated to the flag E∙:={X=Xr⊃Er⊃{q}}, defined by the surface X and the exceptional divisor Er given by any divisorial valuation of the complex projective plane P2, with respect ...
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No-go theorems for photon state transformations in quantum linear optics
Elsevier (2023)We give a necessary condition for photon state transformations in linear optical setups preserving the total number of photons. From an analysis of the algebra describing the quantum evolution, we find a conserved quantity ...
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On the score sheets of a round-robin football tournament
Elsevier (2017-10)The set of (ordered) score sheets of a round-robin football tournament played between n teams together with the pointwise addition has the structure of an affine monoid. In this paper we study (using both theoretical and ...
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Optimal approximation to unitary quantum operators with linear optics
Springer Nature (2021-09-21)Linear optical systems acting on photon number states produce many interesting evolutions, but cannot give all the allowed quantum operations on the input state. Using Toponogov’s theorem from differential geometry, we ...
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Poincaré series for curve singularities and its behaviour under projections
Elsevier (2015)Let O be an equicharacteristic reduced complete noetherian local ring of Krull dimension one, and let S be the value semigroup associated with O. The aim of the paper is to investigate the behaviour of the multi-variable ...
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QOptCraft: A Python package for the design and study of linear optical quantum systems
Elsevier (2022-08-29)The manipulation of the quantum states of light in linear optical systems has multiple applications in quantum optics and quantum computation. The package QOptCraft gives a collection of methods to solve some of the most ...
