Integer points in convex polyhedra

<p>The study of integer points in convex polyhedra is motivated by questions such as "how many nonnegative <a href="/facts/Integer/PUwwrawx">integer</a>-valued solutions does a <a href="/facts/System_of_linear_equations/fk9CFdgp">system of linear equations</a> with nonnegative coefficients have" or "how many solutions does an <a href="/facts/Integer_linear_program/MDaaadoA">integer linear program</a> have". Counting integer points in <a href="/facts/Polyhedra/UC0p9FTF">polyhedra</a> or other questions about them arise in <a href="/facts/Representation_theory/3ydLtaGH">representation theory</a>, <a href="/facts/Commutative_algebra/mKtUdPCT">commutative algebra</a>, <a href="/facts/Algebraic_geometry/rh7RHVp3">algebraic geometry</a>,  <a href="/facts/Statistics/DNPsKGYU">statistics</a>, and <a href="/facts/Computer_science/lN3pEyPz">computer science</a>.
</p><p>The set of integer points, or, more generally, the set of points of an <a href="/facts/Affine_lattice/2ls9Iv9N">affine lattice</a>,  in a polyhedron is called Z-polyhedron, from the mathematical notation 
  
    
      
        
          Z
        
      
    
    {\displaystyle \mathbb {Z} }
  
 or Z for the set of integer numbers.
</p>

Integer points in convex polyhedra open-in-new

Integer points in convex polyhedra