Irrational Proofs for Two Theorems of Stanley
نویسندگان
چکیده
We give new proofs of two theorems of Stanley on generating functions for the integer points in rational cones. The first, Stanley’s reciprocity theorem, relates the rational generating function σv+K(x) := ∑ m∈v+K∩Z x m, where K is a rational cone and v ∈ R, with σ−v+K◦(1/x). The second theorem asserts that the generating function of the Ehrhart quasipolynomial LP(n) := # (
منابع مشابه
Irrational proofs for three theorems of Stanley
We give new proofs of three theorems of Stanley on generating functions for the integer points in rational cones. The first, Stanley’s Reciprocity Theorem, relates the rational generating function σv+K(x) := ∑ m∈v+K∩Z x m, where K is a rational cone and v ∈ R, with σ−v+K◦(1/x). The second, Stanley’s Positivity Theorem, asserts that the generating function of the Ehrhart quasipolynomial LP(n) :=...
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تاریخ انتشار 2005