If A is an nxn matrix, then the permanent of A is the sum of all products of entries on each of n! diagonals of A. Also, A is called doubly stochastic if it has non-negative entries and the row and column sums are all equal to one. A conjecture on the minimum of the permanent on the set of doubly stochastic matrices was stated by van der Waerden in 1926 and became one of the most studied conjectures for permanents. It was open for more than 50 years until, in 1981, Egorychev and Falikman independently settled it. Another conjecture (which, if it were true, would imply the van der Waerden conjecture) was originally stated by Holens in 1964 in his M.Sc. thesis at the University of Manitoba. Three years later, Dokovic independently introduced an equivalent conjecture. This conjecture is now known as the Holens-Dokovic conjecture, and while known not to be true in general, it still remains unresolved for some specific cases. This thesis is devoted to the study of these and other conjectures on permanents.

If A is an nxn matrix, then the permanent of A is the sum of all products of entries on each of n! diagonals of A. Also, A is called doubly stochastic if it has non-negative entries and the row and column sums are all equal to one. A conjecture on the minimum of the permanent on the set of doubly stochastic matrices was stated by van der Waerden in 1926 and became one of the most studied conjectures for permanents. It was open for more than 50 years until, in 1981, Egorychev and Falikman independently settled it. Another conjecture (which, if it were true, would imply the van der Waerden conjecture) was originally stated by Holens in 1964 in his M.Sc. thesis at the University of Manitoba. Three years later, Dokovic independently introduced an equivalent conjecture. This conjecture is now known as the Holens-Dokovic conjecture, and while known not to be true in general, it still remains unresolved for some specific cases. This thesis is devoted to the study of these and other conjectures on permanents.

Made available in DSpace on 2016-12-12T20:15:50Z (GMT). No. of bitstreams: 1 Karla Weber.pdf: 792478 bytes, checksum: 5ad5bec34e3e16a7e56322ccf40af568 (MD5) Previous issue date: 2014-03-18 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / In this work we will show that the wave equations for any twistor fields carrying a single index, which occur in the frameworks of the Infeld-van der Waerden γ formalisms for General Relativity, must be formally the same. This result stems mainly from the fact that the spinor transcription of the traditional conformal Killing equation provides twistor equations of the same form. A consequence of this result is that the usual γ formalism covariant differential devices for controlling valences of spinor-index configurations turn out to be inapplicable as regards the speciation of the formal patterns for the wave equations under consideration here. / Mostraremos neste trabalho que as equações de onda para quaisquer campos twistoriais de um único índice, as quais ocorrem no contexto dos formalismos espinoriais γ de Infeld e van der Waerden para a Relatividade Geral, devem ser formalmente as mesmas. Este resultado decorre essencialmente do fato que a transcrição espinorial da tradicional equação conforme de Killing fornece equações twistoriais da mesma forma. Uma conseqüência deste resultado e que os dispositivos diferenciais covariantes do formalismo γ, os quais usualmente servem para controlar valências de conjurações indiciais, tornam-se inaplicáveis no que concerne a obtenção dos padrões formais das equações de onda sob consideração aqui.

Submitted by Nilton Cesar Moretti Junior null (niiilton@hotmail.com) on 2018-07-31T04:58:47Z No. of bitstreams: 1 Dissertação-Final.pdf: 1149444 bytes, checksum: 6c44dc0b9f2462ee08c23da4a240fa0a (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2018-07-31T18:13:18Z (GMT) No. of bitstreams: 1 morettijunior_nc_me_sjrp.pdf: 1461434 bytes, checksum: 7a6418b1192346448fc927ec6c6650dc (MD5) / Made available in DSpace on 2018-07-31T18:13:18Z (GMT). No. of bitstreams: 1 morettijunior_nc_me_sjrp.pdf: 1461434 bytes, checksum: 7a6418b1192346448fc927ec6c6650dc (MD5) Previous issue date: 2017-08-30 / Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho estudamos vários resultados relacionados com sistemas dinâmicos, teoria dos números e combinatória. Em particular, provamos os teoremas de Van Der Waerden, Szemeredi, Koksma e Weyl. / In this work we study several results connected with dynamical systems, number thoery and combinatorics. In particular, we prove Van Der Waerden, Szemer edi, Koksma and Weyl’s theorems.

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