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