On integer points in polygons
نویسندگان
چکیده
منابع مشابه
On integer points in polyhedra
We give an upper bound on the number of vertices of PI, the integer hull of a polyhedron P, in terms of the dimension n of the space, the number m of inequalities required to describe P, and the size ~ of these inequalities. For fixed n the bound is O(mn~n-1). We also describe an algorithm which determines the number of integer points in a polyhedron to within a multiplicative factor of 1 qE in...
متن کاملOn Sampling Integer Points in Polyhedra
We investigate the problem of sampling integer points in rational polyhedra provided an oracle for counting these integer points. When dimension is bounded, this assumption is justified in view of a recent algorithm due to Barvinok [B1,B2,BP]. We show that the exactly uniform sampling is possible in full generality, when the oracle is called polynomial number of times. Further, when Barvinok’s ...
متن کاملMusical Scales, Integer Partitions, Necklaces, and Polygons
A musical scale can be viewed as a subsequence of notes taken from a chromatic sequence. Given integers (N,K) N > K we use particular integer partitions of N into K parts to construct distinguished scales. We show that a natural geometric realization of these scales results in maximal polygons.
متن کاملInteger points on cubic Thue equations
We prove that there are infinitely many inequivalent cubic binary forms F with content 1 for which the Thue equation F (x, y) = m has ≫ (logm) solutions in integers x and y for infinitely many integers m.
متن کاملS-integer Points on Elliptic Curves
We give a quantitative bound for the number of S-integral points on an elliptic curve over a number field K in terms of the number of primes dividing the denominator of the j-invariant, the degree [K : Q], and the number of primes in S. Let K be a number field of degree d and MK the set of places of K. Let E/K be an elliptic curve with quasi-minimal Weierstrass equation E : y = x +Ax+B. If ∆ = ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1993
ISSN: 0373-0956
DOI: 10.5802/aif.1333