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The formal series Witt transform | | Pieter Moree
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12 Nov 2003 | | Journal: | Discrete Mathematics 295 (2005), 143-160 DOI: 10.1016/j.disc.2005.03.004 | | Subject: | Combinatorics; Number Theory MSC-class: 05A19; 11B75; 17B01 | math.CO math.NT | | Abstract: | Given a formal power series f(z) we define, for any positive integer r, its rth Witt transform, W_f^{(r)}, by rW_f^{(r)}(z)=sum_{d|r}mu(d)f(z^d)^{r/d}, where mu is the Moebius function. The Witt transform generalizes the necklace polynomials M(a,n) that occur in the cyclotomic identity 1-ay=prod (1-y^n)^{M(a,n)}, where the product is over all positive integers. Several properties of the Witt transform are established. Some examples relevant to number theory are considered. | | Source: | arXiv, math.CO/0311194 | | Services: | Forum | Review | PDF | Favorites | |
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