scholarly journals The trees for which maximum multiplicity implies the simplicity of other eigenvalues

2006 ◽  
Vol 306 (23) ◽  
pp. 3130-3135
Author(s):  
Charles R. Johnson ◽  
Carlos M. Saiago
Keyword(s):  
Maximum Multiplicity

A Zero of Maximum Multiplicity

SIAM Review ◽  
1976 ◽  
Vol 18 (4) ◽  
pp. 763-763
Author(s):  
N. Liron
Keyword(s):  
Maximum Multiplicity

scholarly journals Reaching the Maximum Multiplicity of the Covalent Chemical Bond

2007 ◽  
Vol 119 (9) ◽  
pp. 1491-1494 ◽  
Author(s):  
Björn O. Roos ◽  
Antonio C. Borin ◽  
Laura Gagliardi
Keyword(s):  
Chemical Bond ◽  
Covalent Chemical Bond ◽  
Maximum Multiplicity

A Zero Of Maximum Multiplicity (N. Liron and L. A. Rubenfeld)

SIAM Review ◽  
1977 ◽  
Vol 19 (4) ◽  
pp. 743-744
Author(s):  
w. B. Jordan
Keyword(s):  
Maximum Multiplicity

Onn-Sums in an Abelian Group

2015 ◽  
Vol 25 (3) ◽  
pp. 419-435 ◽  
Author(s):  
WEIDONG GAO ◽  
DAVID J. GRYNKIEWICZ ◽  
XINGWU XIA
Keyword(s):  
Abelian Group ◽  
Maximum Multiplicity

LetGbe an additive abelian group, letn⩾ 1 be an integer, letSbe a sequence overGof length |S| ⩾n+ 1, and let${\mathsf h}$(S) denote the maximum multiplicity of a term inS. Let Σn(S) denote the set consisting of all elements inGwhich can be expressed as the sum of terms from a subsequence ofShaving lengthn. In this paper, we prove that eitherng∈ Σn(S) for every termginSwhose multiplicity is at least${\mathsf h}$(S) − 1 or |Σn(S)| ⩾ min{n+ 1, |S| −n+ | supp (S)| − 1}, where |supp(S)| denotes the number of distinct terms that occur inS. WhenGis finite cyclic andn= |G|, this confirms a conjecture of Y. O. Hamidoune from 2003.

scholarly journals The graphs for which the maximum multiplicity of an eigenvalue is two

2009 ◽  
Vol 57 (7) ◽  
pp. 713-736 ◽  
Author(s):  
Charles R. Johnson ◽  
Raphael Loewy ◽  
Paul Anthony Smith
Keyword(s):  
Maximum Multiplicity ◽  
Multiplicity Of An Eigenvalue

scholarly journals On Hau's lemma

1994 ◽  
Vol 50 (3) ◽  
pp. 451-458 ◽  
Author(s):  
W.K.A. Loh
Keyword(s):  
Prime Power ◽  
Main Lemma ◽  
Precise Form ◽  
Image Position ◽  
Maximum Multiplicity

Let f ∈ ℤ[X] and let q be a prime power pl(l ≥ 2). Hua stated and proved thatfor some unspecified constant C > 0 depending on the derivative f′ of f; M denoting the maximum multiplicity of the roots of the congruence p−tf′(x) ≡ 0 (mod p), where t is an integer chosen so that the polynomial p−tf′(x) is primitive. An explicit value for C was given by Chalk for p ≥ 3. Subsequently, Ping Ding (in two successive articles) obtained better estimates for p ≥ 2.This article provides a better result, based upon a more precise form of Hua's main lemma, previously overlooked.

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