CombinatorialOpsCategory

combfunc.spad line 1 [edit on github]

CombinatorialOpsCategory is the category obtaining by adjoining summations and products to the usual combinatorial operations.

binomial: (%, %) -> %

from CombinatorialFunctionCategory

factorial: % -> %

from CombinatorialFunctionCategory

factorials: % -> %

factorials(f) rewrites the permutations and binomials in f in terms of factorials.

factorials: (%, Symbol) -> %

factorials(f, x) rewrites the permutations and binomials in f involving x in terms of factorials.

permutation: (%, %) -> %

from CombinatorialFunctionCategory

product: (%, SegmentBinding %) -> %

product(f(n), n = a..b) returns f(a) * … * f(b) as a formal product.

product: (%, Symbol) -> %

product(f(n), n) returns the formal product P(n) which verifies P(n+1)/P(n) = f(n).

summation: (%, SegmentBinding %) -> %

summation(f(n), n = a..b) returns f(a) + … + f(b) as a formal sum.

summation: (%, Symbol) -> %

summation(f(n), n) returns the formal sum S(n) which verifies S(n+1) - S(n) = f(n).

CombinatorialFunctionCategory