partition property
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10.37236/6977 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Sylwia Cichacz

We will say that an Abelian group $\Gamma$ of order $n$ has the $m$-zero-sum-partition property ($m$-ZSP-property) if $m$ divides $n$, $m\geq 2$ and there is a partition of $\Gamma$ into pairwise disjoint subsets $A_1, A_2,\ldots , A_t$, such that $|A_i| = m$ and $\sum_{a\in A_i}a = g_0$ for $1 \leq i \leq t$, where $g_0$ is the identity element of $\Gamma$.In this paper we study the $m$-ZSP property of $\Gamma$. We show that $\Gamma$ has the $m$-ZSP property if and only if $m\geq 3$ and $|\Gamma|$ is odd or $\Gamma$ has more than one involution. We will apply the results to the study of group distance magic graphs as well as to generalized Kotzig arrays.





2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Christian J. Michel ◽  
Giuseppe Pirillo

We begin here a combinatorial study of dinucleotide circular codes. A word written on a circle is called circular. A set of dinucleotides is a circular code if all circular words constructed with this set have a unique decomposition. Propositions based on a letter necklace allow to determine the 24 maximum dinucleotide circular codes (of 6 elements). A partition property is also identified with eight self-complementary maximum dinucleotide circular codes and two classes of eight maximum dinucleotide circular codes in bijective correspondence by the complementarity map.



2012 ◽  
Vol 51 (5-6) ◽  
pp. 575-589 ◽  
Author(s):  
Yoshihiro Abe ◽  
Toshimichi Usuba
Keyword(s):  


2010 ◽  
Vol 13 (6) ◽  
pp. 1323-1341 ◽  
Author(s):  
John E. Goulionis ◽  
Dimitrios I. Stengos ◽  
George Tzavelas


ChemInform ◽  
2010 ◽  
Vol 28 (51) ◽  
pp. no-no
Author(s):  
B.-H. LEE ◽  
J.-H. SHIN ◽  
M.-K. LIM ◽  
T.-S. JANG ◽  
J.-S. PARK ◽  
...  
Keyword(s):  


2008 ◽  
Vol 12 (2) ◽  
pp. 91-97
Author(s):  
Kazuhiro Ikeda ◽  
Yoshihisa Shimizu ◽  
Saburo Matsui ◽  
Takuya Oguri ◽  
Makoto Sekida ◽  
...  


2008 ◽  
Vol 346 (1-2) ◽  
pp. 10-16 ◽  
Author(s):  
Satyanarayana Valiveti ◽  
James Wesley ◽  
Guang Wei Lu
Keyword(s):  


2005 ◽  
Vol 134 (7) ◽  
pp. 2147-2152 ◽  
Author(s):  
Pierre Matet


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