Carlos Gamas

Universidade de Coimbra, Mathematics, Faculty Member

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Catherine Rowett

University of East Anglia

John Sellars

Royal Holloway, University of London

Armando Marques-Guedes

UNL - New University of Lisbon

Giulia Sissa

Ucla

Prof. Dr. Raffaele Pisano, MSc, HDR (Habil.)

Université des Sciences et Technologies de Lille (Lille-1)

Francesca Gazzano

University of Genova

Sophia Xenophontos

Academy of Athens

Luciana Gabriela Soares Santoprete

Centre National de la Recherche Scientifique / French National Centre for Scientific Research

Patrick Blessinger

St. John's University

Margalit Finkelberg

Tel Aviv University

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Papers by Carlos Gamas

Conditions for a symmetrized decomposable tensor to be zero

Linear Algebra and its Applications, Sep 1, 1988

Let xl* ... *xm he a decomposable symmetrized tensor corresponding to the symmetric group S, and ... more Let xl* ... *xm he a decomposable symmetrized tensor corresponding to the symmetric group S, and an irreducible character X. A necessary and sufficient condition on the vectors xl,.. . , xm is given for x1 * f. . * xrn to be zero. x1*-*-*xm = T(G, X)(x,c%-a. @3x,) and call xi *. .. * x, a decomposable symmetrized tensor. We assume throughout that G = S, and write V, instead of V,(S,). Our objective is the study of the problem of finding conditions for xi *-*-* x, to be equal to zero. When xl,.. . , x, are elements of a basis for V the problem was solved in [ 11. In [2] some necessary and some sufficient conditions were given. In this paper we present a complete solution (theorem below). Let A(a) = (aij(a)) be an irreducible representation of G affording the character X. We put X(id) T,(G, A) =o(G) o~c~ii(u)J'(o)t i = I,..., Atid).

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Spherical functions and immanants

Linear & Multilinear Algebra, Apr 1, 2000

Let λ be an irreducible character of Sn corresponding to the partition (r,s) of n. Let A be a pos... more Let λ be an irreducible character of Sn corresponding to the partition (r,s) of n. Let A be a positive semidefinite Hermitian n × n matrix. Let dλ (A) and per(A) be the immanants corresponding to λ and to the trivial character of Sn , respectively. A proof of the inequality dλ(A)≤λ(id)per(A) is given.

Mathematics in Alexandria: convergence and irradiation

Com este trabalho pretende dar-se um panorama do que foi a actividade cientifica, no dominio da ... more Com este trabalho pretende dar-se um panorama do que foi a actividade cientifica, no dominio da Matematica e das ciencias que lhe andavam ligadas (Geografia, Astronomia, Mecânica), no grande centro cultural que foi o Museu e a Biblioteca de Alexandria, nos tempos aureos e ate ao declinio definitivo da ciencia nesse espaco. Pretende-se igualmente sublinhar as descobertas e progressos que abriram caminho para posteriores estadios de desenvolvimento da Matematica, assim como dar conta do cruzamento de saberes e da grande mobilidade de cientistas matematicos e relacoes entre si, alguns provenientes de muitos espacos e sediados em Alexandria, outros formados em Alexandria e regressados ao seu espaco de origem.

Diophantus and the beginnings of Algebra

Espaços do pensamento científico da Antiguidade, 2013

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Symmetrized Tensors and Spherical Functions

Springer Proceedings in Mathematics & Statistics, 2017

Let G be a subgroup of the symmetric group and \(\varphi \) a complex function on G. A longstandi... more Let G be a subgroup of the symmetric group and \(\varphi \) a complex function on G. A longstanding question in Multilinear Algebra is to find conditions for the vanishing of the decomposable symmetrized tensor associated with G and \(\varphi \) (we recall the definition below). When \(\varphi \) is an irreducible complex character of G, the problem has been studied by several authors, see for example [1, 2, 3, 5]. In the present paper we study and solve the vanishing problem for the case when G is the full symmetric group and \(\varphi \) is a certain type of spherical function .

Conditions for a symmetrized tensor associated with a spherical function to be zero

Linear and multilinear algebra, Dec 10, 2017

ABSTRACT Let be an irreducible character of . Let and let be an irreducible character of . Suppos... more ABSTRACT Let be an irreducible character of . Let and let be an irreducible character of . Suppose that is minimal of the set relatively to the dominance order in the set of partitions of m, where denotes the set of all irreducible characters of . Let be the spherical function associated with and . A necessary and sufficient condition on the vectors is given for to be zero.

On the conjecture of Alon-Tarsi

The Alon-Tarsi Conjecture states that for even n, the number of even latin squares of order n dif... more

The Great Advances in Mathematics in the Context of Alexandrian Culture

Alexandrea ad Aegyptvm: the legacy of multiculturalismo in antiquity, 2013

A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitali... more A navegação consulta e descarregamento dos títulos inseridos nas Bibliotecas Digitais UC Digitalis, UC Pombalina e UC Impactum, pressupõem a aceitação plena e sem reservas dos Termos e Condições de Uso destas Bibliotecas Digitais, disponíveis em https://digitalis.uc.pt/pt-pt/termos. Conforme exposto nos referidos Termos e Condições de Uso, o descarregamento de títulos de acesso restrito requer uma licença válida de autorização devendo o utilizador aceder ao(s) documento(s) a partir de um endereço de IP da instituição detentora da supramencionada licença. Ao utilizador é apenas permitido o descarregamento para uso pessoal, pelo que o emprego do(s) título(s) descarregado(s) para outro fim, designadamente comercial, carece de autorização do respetivo autor ou editor da obra. Na medida em que todas as obras da UC Digitalis se encontram protegidas pelo Código do Direito de Autor e Direitos Conexos e demais legislação aplicável, toda a cópia, parcial ou total, deste documento, nos casos em que é legalmente admitida, deverá conter ou fazer-se acompanhar por este aviso.

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De Alexandria ao Islão: a tradução algébrica de Euclides e a convergência de saberes matemáticos na Casa da Sabedoria

Archai: Revista de Estudos sobre as Origens do Pensamento Ocidental, 2015

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Diofanto de Alexandria e os primórdios da Álgebra

This chapter aims to consider the nature of Diophantus' mathematical research in what concerns th... more This chapter aims to consider the nature of Diophantus' mathematical research in what concerns the potential origins of Algebra and to make it understandable in the context of a former eastern-western tradition, as much as in the context of the latter Islamic reception. It is to underline that Algebra attains its autonomy and maturity in the Islamic world and that Diophantus and the Greek tradition stay as one of the forerunners of Algebra.

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