Talk:Ehrhart polynomial
From Wikipedia, the free encyclopedia
The polytope being "integral" means that all its corners are lattice points? AxelBoldt 20:03, 16 Feb 2004 (UTC)
Anyway, I blanked the page since it was a copyright violation; the text was a verbatim copy of http://mathworld.wolfram.com/EhrhartPolynomial.html . Somebody should rephrase that material and write it up again. AxelBoldt 02:25, 18 Feb 2004 (UTC)
[edit] Ehrhart's theorem for non-convex polytopes
Usually Ehrhart's theorem is stated for convex polytopes, but here convexity is not stated. Is that correct? McKay 16:17, 4 August 2006 (UTC)
Good point--the polynomiality theorem still holds, but Ehrhart reciprocity needs a stronger condition, e.g., the polytope being homeomorphic to a manifold is good enough. For simplicity, I inserted the condition that the polytope is convex. Mattbeck 04:18, 14 August 2006 (UTC)
- Thanks. Do you happen to know where more general conditions are investigated? McKay 08:01, 15 August 2006 (UTC)
-
- Try Peter McMullen's papers, e.g., Valuations and Euler-type relations on certain classes of convex polytopes, Proc. London Math. Soc. (3) 35, no. 1 (1977), 113-135, or Lattice invariant valuations on rational polytopes, Arch. Math. 31, no. 5 (1978), 509-516. Another good starting point might be Richard Stanley, Combinatorial reciprocity theorems, Advances in Math. 14 (1974), 194-253. Mattbeck 23:43, 15 August 2006 (UTC)
- Thanks, I'll check those out. --McKay 04:18, 16 August 2006 (UTC)
- Try Peter McMullen's papers, e.g., Valuations and Euler-type relations on certain classes of convex polytopes, Proc. London Math. Soc. (3) 35, no. 1 (1977), 113-135, or Lattice invariant valuations on rational polytopes, Arch. Math. 31, no. 5 (1978), 509-516. Another good starting point might be Richard Stanley, Combinatorial reciprocity theorems, Advances in Math. 14 (1974), 194-253. Mattbeck 23:43, 15 August 2006 (UTC)
