Return to Answer

For a polynomial-time method of counting integer lattice points for the n-simplex:

Review article - Crites, A., Goff, M., Korson, M., Patrolia, L., Wolcott, L. "Counting Lattice Points in Polyhedra."

Available here with references for Barvinok's 1994 & 1999 algorithms - http://www.math.washington.edu/~thomas/teaching/m583_s2008_web/Barvinok.pdf

For an implementation of Barvinok's algorithm, see J.A. De Loera's LattE program (hosted at UC Davis): http://www.math.ucdavis.edu/~latte/group.htm

For a polynomial-time method of counting integer lattice points for the n-simplex (with fixed dimension):

Review article - Crites, A., Goff, M., Korson, M., Patrolia, L., Wolcott, L. "Counting Lattice Points in Polyhedra."

Available here with references for Barvinok's 1994 & 1999 algorithms - http://www.math.washington.edu/~thomas/teaching/m583_s2008_web/Barvinok.pdf

For an implementation of Barvinok's algorithm, see J.A. De Loera's LattE program (hosted at UC Davis): http://www.math.ucdavis.edu/~latte/group.htm

Answer to first part of question concerning a (polynomial-time) method of counting integer lattice points for the n-simplex:

Review article - Crites, A., Goff, M., Korson, M., Patrolia, L., Wolcott, L. "Counting Lattice Points in Polyhedra."

Available here with references for Barvinok's 1994 & 1999 algorithms - http://www.math.washington.edu/~thomas/teaching/m583_s2008_web/Barvinok.pdf

For an implementation of Barvinok's algorithm, see J.A. De Loera's LattE program (hosted at UC Davis): http://www.math.ucdavis.edu/~latte/group.htm

For a polynomial-time method of counting integer lattice points for the n-simplex:

Review article - Crites, A., Goff, M., Korson, M., Patrolia, L., Wolcott, L. "Counting Lattice Points in Polyhedra."

Available here with references for Barvinok's 1994 & 1999 algorithms - http://www.math.washington.edu/~thomas/teaching/m583_s2008_web/Barvinok.pdf

For an implementation of Barvinok's algorithm, see J.A. De Loera's LattE program (hosted at UC Davis): http://www.math.ucdavis.edu/~latte/group.htm

Answer to first part of question concerning a (polynomial-time) method of counting integer lattice points for the n-simplex:

Review article - Crites, A., Goff, M., Korson, M., Patrolia, L., Wolcott, L. "Counting Lattice Points in Polyhedra."

Available here with references for Barvinok's 1994 & 1999 algorithms - http://www.math.washington.edu/~thomas/teaching/m583_s2008_web/Barvinok.pdf

Answer to first part of question concerning a (polynomial-time) method of counting integer lattice points for the n-simplex:

Review article - Crites, A., Goff, M., Korson, M., Patrolia, L., Wolcott, L. "Counting Lattice Points in Polyhedra."

Available here with references for Barvinok's 1994 & 1999 algorithms - http://www.math.washington.edu/~thomas/teaching/m583_s2008_web/Barvinok.pdf

For an implementation of Barvinok's algorithm, see J.A. De Loera's LattE program (hosted at UC Davis): http://www.math.ucdavis.edu/~latte/group.htm