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On a weighted zero-sum constant related to the Jacobi symbol | | Santanu Mondal
; Krishnendu Paul
; Shameek Paul
; | | Date: |
1 Jan 2022 | | Abstract: | For a finite abelian group $(G,+)$ of exponent $mgeq 2$ and for a non-empty
set $Asubseteq{1,2,ldots,m-1}$, the $A$-weighted zero-sum constant $C_A(G)$
is defined to be the smallest natural number $k$, such that any sequence of $k$
elements in $G$ has a subsequence of consecutive terms such that some
$A$-linear combination of its terms is zero (the identity element). We consider
the group $mathbb Z_n$ and take $A$ to be the kernel of the map given by the
Jacobi symbol. For a prime divisor $p$ of $n$, we also consider the set
$ig{xin mathbb Z_nmid x~ extrm{is a unit
and}~ig(frac{x}{n}ig)=ig(frac{x}{p}ig)ig}$ as a weight set. | | Source: | arXiv, 2201.00127 | | Services: | Forum | Review | PDF | Favorites | |
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