macaulayRep -- the Macaulay representation of an integer

Synopsis

Usage:

h=macaulayRep(a,d)
Inputs:
- a, an integer, a nonnegative integer
- d, an integer, a positive integer
Outputs:
- L, a list, a list of pairs {i,j} of integers such that j <= d for all terms, and a is the sum of the binomial(i,j).

Description

Yields the d-th Macaulay representation of the integer a. Given a positive integer d, each positive integer a can be uniquely represented as a sum of binomials binomial(b_d,d) + binomial(b_{d-1},d-1) + ... + binomial(b_1,1), where b_d > b_{d-1} > ... > b_1 >= 0.

i1 : macaulayRep(100,4)

o1 = {{8, 4}, {6, 3}, {5, 2}}

o1 : List

i2 : macaulayRep(10,5)

o2 = {{6, 5}, {4, 4}, {3, 3}, {2, 2}, {1, 1}}

o2 : List

Ways to use macaulayRep :

macaulayRep(ZZ,ZZ)

For the programmer

The object macaulayRep is a method function.

macaulayRep -- the Macaulay representation of an integer

Synopsis

Description

See also

Ways to use macaulayRep :

For the programmer