On Davenport's Constant

Rath, Purusottam; Srilakshmi, K.; Thangadurai, R.

doi:10.1142/s1793042108001195

Cited by 3 publications

(2 citation statements)

References 18 publications

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“…Let d(G) denote the maximal length of a zero-sum free sequence over G. Then d(G) + 1 is the Davenport constant of G, a classical constant from Combinatorial Number Theory (for surveys and historical comments, the reader is referred to [3], [8,Chapter 5], [7]). In general, the precise value of d(G) (in terms of the group invariants of G) and the structure of the extremal sequences is unknown, see [12,1,13,10,11,4,14,15,9] for recent progress.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On the Davenport constant and group algebras

Smertnig

2010

Colloq. Math.

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For a finite abelian group $G$ and a splitting field $K$ of $G$, let $d(G, K)$ denote the largest integer $l \in \N$ for which there is a sequence $S = g_1 \cdot ... \cdot g_l$ over $G$ such that $(X^{g_1} - a_1) \cdot ... \cdot (X^{g_l} - a_l) \ne 0 \in K[G]$ for all $a_1, ..., a_l \in K^{\times}$. If $D(G)$ denotes the Davenport constant of $G$, then there is the straightforward inequality $D(G)-1 \le d (G, K)$. Equality holds for a variety of groups, and a standing conjecture of W. Gao et.al. states that equality holds for all groups. We offer further groups for which equality holds, but we also give the first examples of groups $G$ for which $D(G) -1 < d(G, K)$ holds. Thus we disprove the conjecture.Comment: 12 pages; fixed typos and clearer proof of Lemma 3.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

On the Davenport constant and group algebras

Smertnig

2010

Colloq. Math.

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“…The best known upper bound is due to Emde Boas and Kruswjik [6,Theorem 7.1,p. 19], Meshulam [15], Alford et al [1] and Rath et al [19] which is as follows…”

Section: Introductionmentioning

confidence: 99%

New upper bounds for the Davenport and for the Erdős–Ginzburg–Ziv constants

Chintamani¹,

Moriya²,

Gao

et al. 2012

Arch. Math.

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Let G be a finite abelian group (written additively) of rank r with invariants n1, n2, . . . , nr, where nr is the exponent of G. In this paper, we prove an upper bound for the Davenport constant D(G) of G as follows; D(G) ≤ nr + nr−1 + (c(3) − 1)nr−2 + (c(4) − 1)nr−3 + · · · + (c(r) − 1)n1 + 1, where c(i) is the Alon-Dubiner constant, which depends only on the rank of the group Z i nr . Also, we shall give an application of Davenport's constant to smooth numbers related to the Quadratic sieve.Mathematics Subject Classification (2010). Primary 11B75; Secondary 20K01.

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Analytic number theory in India during 2001–2010

Munshi

2019

Indian J Pure Appl Math

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On Davenport's Constant

Cited by 3 publications

References 18 publications

On the Davenport constant and group algebras

On the Davenport constant and group algebras

New upper bounds for the Davenport and for the Erdős–Ginzburg–Ziv constants

Analytic number theory in India during 2001–2010

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