Irrational proofs for three theorems of Stanley Academic Article uri icon

abstract

  • We give new proofs of three theorems of Stanley on generating functions for the integer points in rational cones. The first relates the rational generating function v + K (x) {colon equals} m (v + K) Zd xm, where K is a rational cone and v Rd, with - v + K{ring operator} (1 / x). The second theorem asserts that the generating function 1 + n 1 LP (n) tn of the Ehrhart quasi-polynomial LP (n) {colon equals} # (n P Zd) of a rational polytope P can be written as a rational function frac(P (t), (1 - t)dim P + 1) with nonnegative numerator P. The third theorem asserts that if P Q, then P Q. Our proofs are based on elementary counting afforded by irrational decompositions of rational polyhedra. 2005 Elsevier Ltd. All rights reserved.

published proceedings

  • European Journal of Combinatorics

altmetric score

  • 3

author list (cited authors)

  • Beck, M., & Sottile, F.

citation count

  • 13

complete list of authors

  • Beck, Matthias||Sottile, Frank

publication date

  • January 2007