On balanced Cayley maps over abelian groups

2008 ◽  
Vol 31 ◽  
pp. 115-118 ◽  
Author(s):  
Mikhail Muzychuk
Keyword(s):  
Abelian Groups ◽  
Cayley Maps

scholarly journals Reflexibility of regular Cayley maps for abelian groups

2009 ◽  
Vol 99 (1) ◽  
pp. 254-260 ◽  
Author(s):  
Marston D.E. Conder ◽  
Young Soo Kwon ◽  
Jozef Širáň
Keyword(s):  
Abelian Groups ◽  
Cayley Maps

scholarly journals Regular t-balanced Cayley maps for abelian groups

2011 ◽  
Vol 311 (21) ◽  
pp. 2309-2316 ◽  
Author(s):  
Rongquan Feng ◽  
Robert Jajcay ◽  
Yan Wang
Keyword(s):  
Abelian Groups ◽  
Cayley Maps

scholarly journals Regular Cayley maps for finite abelian groups

2006 ◽  
Vol 25 (3) ◽  
pp. 259-283 ◽  
Author(s):  
Marston Conder ◽  
Robert Jajcay ◽  
Thomas Tucker
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Cayley Maps

Additive bases via Fourier analysis

2021 ◽  
pp. 1-12
Author(s):  
Bodan Arsovski
Keyword(s):  
Abelian Group ◽  
Fourier Analysis ◽  
Vector Space ◽  
Abelian Groups ◽  
Finite Abelian Group ◽  
Probabilistic Method ◽  
Additive Basis ◽  
Generating Sets

Abstract Extending a result by Alon, Linial, and Meshulam to abelian groups, we prove that if G is a finite abelian group of exponent m and S is a sequence of elements of G such that any subsequence of S consisting of at least $$|S| - m\ln |G|$$ elements generates G, then S is an additive basis of G . We also prove that the additive span of any l generating sets of G contains a coset of a subgroup of size at least $$|G{|^{1 - c{ \in ^l}}}$$ for certain c=c(m) and $$ \in = \in (m) < 1$$ ; we use the probabilistic method to give sharper values of c(m) and $$ \in (m)$$ in the case when G is a vector space; and we give new proofs of related known results.

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