Root geometry of polynomial sequences I: Type (0, 1)

Jonathan L. Gross, Toufik Mansour, Thomas W. Tucker, David G.L. Wang

Research output: Contribution to journalArticlepeer-review


This paper concerns the distribution in the complex plane of the roots of a polynomial sequence {Wn(x)}n≥0 given by a recursion Wn(x)=aWn-1(x)+(bx+c)Wn-2(x), with W0(x)=1 and W1(x)=t(x-r), where a>0, b>0, and c, t, r∈R. Our results include proof of the distinct-real-rootedness of every such polynomial Wn(x), derivation of the best bound for the zero-set {x|Wn(x)=0for some n≥1}, and determination of three precise limit points of this zero-set. Also, we give several applications from combinatorics and topological graph theory.

Original languageAmerican English
Article number19736
Pages (from-to)1261-1289
Number of pages29
JournalJournal of Mathematical Analysis and Applications
Issue number2
StatePublished - 15 Jan 2016


  • Genus distribution
  • Real-rooted polynomial
  • Recurrence
  • Root geometry

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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