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TSpreadIdeals > tMacaulayExpansion

tMacaulayExpansion -- compute the t-Macaulay expansion of a positive integer

Synopsis

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

See also

Ways to use tMacaulayExpansion :

For the programmer

The object tMacaulayExpansion is a method function with options.