Integer polygons of given perimeter

20 Nov 2018 East James Niles Ron

A classical result of Honsberger states that the number of incongruent triangles with integer sides and perimeter $n$ is the nearest integer to $\frac{n^2}{48}$ ($n$ even) or $\frac{(n+3)^2}{48}$ ($n$ odd). We solve the analogous problem for $m$-gons (for arbitrary but fixed $m\geq3$), and for polygons (with arbitrary number of sides)... (read more)

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Categories


  • COMBINATORICS
  • GROUP THEORY