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Full-Text Articles in Number Theory
Commutative N-Ary Arithmetic, Aram Bingham
Commutative N-Ary Arithmetic, Aram Bingham
University of New Orleans Theses and Dissertations
Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Higher order operations yield wider factorization and representation possibilities which correspond to reductions in the set of primes …
Polynomials Occuring In Generating Function Identities For B-Ary Partitions, David Dakota Blair
Polynomials Occuring In Generating Function Identities For B-Ary Partitions, David Dakota Blair
Graduate Student Publications and Research
Let p_b(n) be the number of integer partitions of n whose parts are powers of b. For each m there is a generating function identity:
f_m(b,q)\sum_{n} p_b(n) q^n = (1-q)^m \sum_{n} p_b(b^m n q)q^n
where n ranges over all integer values. The proof of this identity appears in the doctoral thesis of the author. For more information see http://dakota.tensen.net/2015/rp/.
This dataset is a JSON object with keys m from 1 to 23 whose values are f_m(b,q).