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Davenport constant for semigroups II [article]

Guoqing Wang
2015 arXiv   pre-print
The Davenport constant of S, denoted D(S), is defined to be the least positive integer ℓ such that every sequence T of elements in S of length at least ℓ contains a proper subsequence T' (T'≠ T) with the  ...  Let q>2 be a prime power, and let _q[x] be the ring of polynomials over the finite field _q. Let R be a quotient ring of _q[x] with 0≠ R≠_q[x].  ...  Acknowledgements The author would like to thank the referee for his/her very useful suggestions.  ... 
arXiv:1409.2077v3 fatcat:upe637nu6bfkvkpqzq64y3sg2u

Upper Bounds for the Davenport Constant [article]

R. Balasubramanian
2006 arXiv   pre-print
For groups of order three we improve on the existing bound involving the Alon-Dubiner constant.  ...  We prove that for all but a certain number of abelian groups of order n its Davenport constant is atmost n/k+k-1 for k=1,2,..,7.  ...  The authors are grateful to CEFIPRA (Project 2801-1) for their financial support for visits to each others' institute.  ... 
arXiv:math/0601374v3 fatcat:oxajuiu32zdvjkfq5d2utzzku4

On Davenport constant of finite abelian groups [article]

Dongchun Han
2018 arXiv   pre-print
G be an additive finite abelian group. The Davenport constant D(G) is the smallest integer t such that every sequence (multiset) S over G of length |S|> t has a non-empty zero-sum subsequence.  ...  Furthermore, we can get better estimates of the error term for some n of special types. Finally, we get an asymptotic result for some finite abelian groups of special types.  ...  This work has been supported by the National Science Foundation of China Grant No.11601448 and the Fundamental Research Funds for the Central Universities Grant No.2682016CX121.  ... 
arXiv:1802.07196v2 fatcat:g72y73ub35gbzbmowkjvdlyjzi

The zero-sum constant, the Davenport constant and their analogues

Maciej Zakarczemny
2020 Technical Transactions  
Let D(G) be the Davenport constant of a finite Abelian group G.  ...  At the end, we apply the Davenport constant to smooth numbers and make a natural conjecture in the non-Abelian case.  ...  The precise value of the Davenport constant is known, among others, for p-groups and for groups of rank at most two.  ... 
doi:10.37705/techtrans/e2020027 fatcat:m6ojdahktnhb7gpnnekzmvhz2m

An upper bound for Davenport constant of finite groups [article]

Weidong Gao, Yuanlin Li, Jiangtao Peng
2013 arXiv   pre-print
We prove that d(G)≤|G|/p+9p^2-10p, where d(G) denotes the small Davenport constant of G which is defined as the maximal integer ℓ such that there is a sequence over G of length ℓ contains no nonempty one-product  ...  Let G be a finite (not necessarily abelian) group and let p=p(G) be the smallest prime number dividing |G|.  ...  The research was carried out during a visit by the second author to the Center for Combinatorics at Nankai University.  ... 
arXiv:1308.2364v1 fatcat:cwjuwmqmdzgx7d43eae3726pce

Erdős-Ginzburg-Ziv theorem for finite commutative semigroups [article]

Sukumar Das Adhikari, Weidong Gao, Guoqing Wang
2013 arXiv   pre-print
Define the Davenport constant D(S) of S to be the least positive integer d such that every sequence T over S of length at least d contains a proper subsequence T' with σ(T')=σ(T), and define the Erdős-Ginzburg-Ziv  ...  We provide a positive answer to the question above for some classes of finite commutative semigroups, including group-free semigroups, elementary semigroups, and archimedean semigroups with certain constraints  ...  This work was initiated during the first author visited the Center for Combinatorics of Nankai University in 2010, he would like to thank the host's hospitality.  ... 
arXiv:1309.5588v2 fatcat:vqqeivo6jzbvvndia2mh3ij52a

Erdős-Ginzburg-Ziv theorem and Noether number for C_m_φ C_mn [article]

Dongchun Han, Hanbin Zhang
2017 arXiv   pre-print
The small Davenport constant d(G) is the maximal length of a product-one free sequence over G.  ...  Let G be a multiplicative finite group and S=a_1·...· a_k a sequence over G. We call S a product-one sequence if 1=∏_i=1^ka_τ(i) holds for some permutation τ of {1,...,k}.  ...  The small Davenport constant, denoted by d(G), is the maximal length of a product-one free sequence over G.  ... 
arXiv:1707.03639v1 fatcat:iep6c5d5bncrfk4owfoivq642y

Davenport constant of the multiplicative semigroup of the ring Z_n_1⊕...⊕Z_n_r [article]

Guoqing Wang, Weidong Gao
2016 arXiv   pre-print
Given a finite commutative semigroup S (written additively), denoted by D(S) the Davenport constant of S, namely the least positive integer ℓ such that for any ℓ elements s_1,...  ...  Moreover, let S_R be the multiplicative semigroup of the ring R, and U(S_R) the group of units of S_R.  ...  As first, we wish to give a precise result of the Davenport constant, however, we failed.  ... 
arXiv:1603.06030v1 fatcat:qukb2y2qlfaqlicgolwq6ilg6a

Page 20 of Mathematical Reviews Vol. , Issue 98F [page]

1998 Mathematical Reviews  
The Davenport constant D(G) [resp. the zero-sum con- stant ZS(G)] of a finite abelian group G is the least integer ¢ such that every sequence of elements of G with length ¢ has a subse- quence [resp. a  ...  Such bounds are useful because a group with a higher degree of com- mutativity will have a relatively simpler structure. The new bounds improve on previous ones when p is small compared to m.  ... 

Page 3661 of Mathematical Reviews Vol. , Issue 89G [page]

1989 Mathematical Reviews  
This supports Kogan’s more general finiteness conjecture (e.g., cf. the survey article of A. V.  ...  A modified ver- sion of Siegel’s conjecture for these special forms, first mentioned by Bombieri, would be that the number of solutions of the Thue equation F(x,y) =A may be bounded in terms of s and A  ... 

Open problems in additive combinatorics [chapter]

Ernest Croot, Vsevolod Lev
2007 CRM Proceedings and Lecture notes AMS  
A brief historical introduction to the subject of additive combinatorics and a list of challenging open problems, most of which are contributed by the leading experts in the area, are presented.  ...  Acknowledgement Some of the problems presented in this paper originate from the list, compiled by the present authors as a follow-up to the Workshop on Recent Trends in Additive Combinatorics, organized  ...  We are grateful to these institutions for bringing together a large number of distinguished mathematicians, which ultimately allowed us to write this paper.  ... 
doi:10.1090/crmp/043/10 fatcat:llqfcrpr2ja2baryr75c3o357u

The Weighted Davenport constant of a group and a related extremal problem II [article]

Niranjan Balachandran, Eshita Mazumdar
2019 arXiv   pre-print
is no such A), where D_A(G) denotes the A-weighted Davenport constant of the group G.  ...  For a finite abelian group G with (G)=n and an integer k> 2, Balachandran and Mazumdar introduced the extremal function _G(k) which is defined to be min{|A|: ∅≠ A⊆[1,n-1]with D_A(G)< k} (and ∞ if there  ...  The A-weighted Davenport constant of the group G (introduced in Adhikari et al, see [1] ) is the least positive integer k for which the following holds: Given an arbitrary sequence (x 1 , . . . , x k  ... 
arXiv:1912.07509v1 fatcat:4c3zbklxxjf5toyulyib3kfhxu

An application of coding theory to estimating Davenport constants [article]

Alain Plagne, Wolfgang A. Schmid
2010 arXiv   pre-print
For j a positive integer (the case j=1, is the classical one) and a finite Abelian group (G,+,0), the invariant _j(G) is defined as the smallest ℓ such that each sequence over G of length at least ℓ has  ...  We use our results to give improved bounds for the classical Davenport constant of certain groups.  ...  Acknowledgment The authors would like to thank G. Cohen for helpful discussions.  ... 
arXiv:1007.0259v1 fatcat:npbpty6nxjezpgt3qfcfg43fuy

An application of coding theory to estimating Davenport constants

Alain Plagne, Wolfgang A. Schmid
2010 Designs, Codes and Cryptography  
For j a positive integer (the case j = 1, is the classical one) and a finite Abelian group (G, +, 0), the invariant D j (G) is defined as the smallest such that each sequence over G of length at least  ...  We use our results to give improved bounds for the classical Davenport constant of certain groups.  ...  Acknowledgment The authors would like to thank G. Cohen for helpful discussions.  ... 
doi:10.1007/s10623-010-9441-5 fatcat:quw4fveoibhldc72icw6otqcgi

The Noether numbers and the Davenport constants of the groups of order less than 32

Kálmán Cziszter, Mátyás Domokos, István Szöllősi
2018 Journal of Algebra  
For each of these groups the Noether number is greater than the small Davenport constant, whereas the first example of a group whose Noether number exceeds the large Davenport constant is found, answering  ...  Algorithms are developed and used to determine the small and large Davenport constants of these groups.  ...  Given an arbitrary finite group G, Algorithm 1 computes the small Davenport constant.  ... 
doi:10.1016/j.jalgebra.2018.02.040 fatcat:ajqzk5yunnh7zevqzs55q63aia
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