Result: The formal series Witt transform
Title:
The formal series Witt transform
Authors:
Source:
Discrete Mathematics. 295:143-160
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2005.
Publication Year:
2005
Subject Terms:
11B75, Mathematics - Number Theory, Identities, free Lie (super)algebras, Lyndon words, 0102 computer and information sciences, cyclotomic identity, 01 natural sciences, 17B01, Theoretical Computer Science, 05A19, necklace polynomial, Other combinatorial number theory, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Combinatorics (math.CO), Number Theory (math.NT), 0101 mathematics, Combinatorial identities, bijective combinatorics
Document Type:
Academic journal
Article
File Description:
application/xml; application/pdf
Language:
English
ISSN:
0012-365X
DOI:
10.1016/j.disc.2005.03.004
DOI:
10.48550/arxiv.math/0311194
Access URL:
http://arxiv.org/abs/math/0311194
https://arxiv.org/pdf/math/0311194.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0012365X05001020
http://ui.adsabs.harvard.edu/abs/2003math.....11194M/abstract
https://www.sciencedirect.com/science/article/pii/S0012365X05001020
https://pure.uva.nl/ws/files/4076156/164745_238164.pdf
https://arxiv.org/abs/math/0311194
https://arxiv.org/pdf/math/0311194.pdf
https://www.sciencedirect.com/science/article/abs/pii/S0012365X05001020
http://ui.adsabs.harvard.edu/abs/2003math.....11194M/abstract
https://www.sciencedirect.com/science/article/pii/S0012365X05001020
https://pure.uva.nl/ws/files/4076156/164745_238164.pdf
https://arxiv.org/abs/math/0311194
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....60b45c10b710015ab113b4d809929fac
Database:
OpenAIRE
Further Information
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.
18 pages, small improvements in contents and presentation, to appear in Discrete Mathematics