Description
Given four positive integers
(a,n,d,t) there is a unique expression of
a as a sum of binomials $a=\binom{a_d}{d} + \binom{a_{d-1}}{d-1} + \cdots + \binom{a_j}{j}.$ where $a_i > a_{i-1} > \cdots > a_j > j >= 1.$
If the optional parameter
Shift is
true, then the method
tMacaulayExpansion(a,n,d,t,Shift=>true) returns the shifted t-Macaulay expansion of
a, that is, $a^{(d)}=\binom{a_d}{d+1} + \binom{a_{d-1}}{d} + \cdots + \binom{a_j}{j+1}.$To obtain the sum of the binomial coefficients represented in the output list, one can use the method
solveBinomialExpansion. Examples:
i1 : tMacaulayExpansion(50,12,2,1)
o1 = {{10, 2}, {5, 1}}
o1 : List
|
i2 : tMacaulayExpansion(50,12,2,1,Shift=>true)
o2 = {{10, 3}, {5, 2}}
o2 : List
|
i3 : tMacaulayExpansion(50,12,2,2,Shift=>true)
o3 = {{9, 3}, {4, 2}}
o3 : List
|