Artículo
Milne's volume function and vector symmetric polynomials
Autor/es | Briand, Emmanuel
Rosas Celis, Mercedes Helena |
Departamento | Universidad de Sevilla. Departamento de álgebra |
Fecha de publicación | 2009-05 |
Fecha de depósito | 2016-05-31 |
Publicado en |
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Resumen | The number of real roots of a system of polynomial equations
fitting inside a given box can be counted using a vector symmetric
polynomial introduced by P. Milne, the volume function. We provide
the expansion of Milne’s ... The number of real roots of a system of polynomial equations fitting inside a given box can be counted using a vector symmetric polynomial introduced by P. Milne, the volume function. We provide the expansion of Milne’s volume function in the basis of monomial vector symmetric functions, and observe that only monomial functions of a particular kind appear in the expansion, the squarefree monomial functions. By means of an appropriate specialization of the vector symmetric Newton identities, we derive an inductive formula that expresses the squarefree monomial functions in the power sums basis. As a corollary, we obtain an inductive formula that writes Milne’s volume function in the power sums basis. The lattice of the sub–hypergraphs of an hypergraph appears in a natural way in this setting. |
Agencias financiadoras | Ministerio de Educación y Ciencia (MEC). España |
Cita | Briand, E. y Rosas Celis, M.H. (2009). Milne's volume function and vector symmetric polynomials. Journal of symbolic computation, 44 (5), 583-590. |
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