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    Recurrence Relations, Partitions, Generating Functions, Monomials and Noncommutative Algebraic Structure

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    4. In noncommutative algebra, the term monomial refers to any arrangement of a sequence of variables from a set. For example, in a noncommutative algebraic structure on a set of four variables, {x,y,z,w} , examples of monomials of length
    3 are xxx,xyx,xxy,zwy,wzx........

    a) Write a generating function for the number of monomials of length, n, in a noncommutative algebraic structure on a set of four variables.
    b) Find the number of monomials of length, n, in a noncommutative algebraic structure on a set of four variables.

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    https://brainmass.com/math/recurrence-relation/recurrence-relations-partitions-generating-functions-60038

    Solution Preview

    Proof:
    (a) Let f be the generating function for the number of monomials of length n, in a noncommutative algebraic structure on a set of four variables {x,y,z,w}
    When n=1, f(n)=4. There are only 4 cases: ...

    Solution Summary

    Recurrence Relations, Partitions, Generating Functions, Monomials and Noncommutative Algebraic Structure are investigated.

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