Grace-like polynomials

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dc.creatorRuelle, David
dc.date2000-09-20
dc.date.accessioned2026-07-07T04:28:01Z
dc.date.available2026-07-07T04:28:01Z
dc.descriptionResults of somewhat mysterious nature are known on the location of zeros of certain polynomials associated with statistical mechanics (Lee-Yang circle theorem) and also with graph counting. In an attempt at clarifying the situation we introduce and discuss here a natural class of polynomials. Let $P(z_1,...,z_m,w_1,...,w_n)$ be separately of degree 1 in each of its $m+n$ arguments. We say that $P$ is a Grace-like polynomial if $P(z_1,...,w_n)\ne0$ whenever there is a circle in ${\bf C}$ separating $z_1,...,z_m$ from $w_1,...,w_n$. A number of properties and characterizations of these polynomials are obtained.
dc.description14 pages
dc.identifierhttps://arxiv.org/abs/math-ph/0009030
dc.identifierhttp://arxiv.org/abs/math-ph/0009030
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56634
dc.subjectMathematical Physics
dc.titleGrace-like polynomials
dc.typetext

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