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SUMMARY:Kare Gjaldbaek (CUNY Graduate Center)
DTSTART:20200602T133000Z
DTEND:20200602T135500Z
DTSTAMP:20260423T011223Z
UID:CANT2020/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2020/16/
 ">Noninjectivity of nonzero discriminant polynomials and applications to p
 acking polynomials</a>\nby Kare Gjaldbaek (CUNY Graduate Center) as part o
 f Combinatorial and additive number theory (CANT 2021)\n\n\nAbstract\nWe s
 how that an integer-valued quadratic polynomial on $\\mathbb{R}^2$\ncan no
 t be injective on the integer lattice points of any subset of $\\mathbb{R}
 ^2$\ncontaining an affine convex cone if its discriminant is nonzero.\nA c
 onsequence is the non-existence of quadratic packing polynomials\non irrat
 ional sectors of $\\mathbb{R}^2$.\nThe result also simplifies a classical 
 proof of the Fueter-Pólya Theorem\, \nwhich states that the two Cantor po
 lynomials are the only\nquadratic polynomials bijectively mapping $\\mathb
 b{N}_0^2$ onto $\\mathbb{N}_0$.\n
LOCATION:https://researchseminars.org/talk/CANT2020/16/
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