scholarly journals Modular invariance property of association schemes, type II codes over finite rings and finite abelian groups and reminiscences of François Jaeger (a survey)

1999 ◽  
Vol 49 (3) ◽  
pp. 763-782 ◽  
Author(s):  
Eiichi Bannai
Keyword(s):  
Abelian Groups ◽  
Association Schemes ◽  
Invariance Property ◽  
Modular Invariance ◽  
Type Ii ◽  
Finite Abelian Groups ◽  
Finite Rings ◽  
Type Ii Codes

scholarly journals Counting Compositions over Finite Abelian Groups

10.37236/7591 ◽  
2018 ◽  
Vol 25 (2) ◽  
Author(s):  
Zhicheng Gao ◽  
Andrew MacFie ◽  
Qiang Wang
Keyword(s):  
Transfer Matrix ◽  
Finite Fields ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Abelian Groups ◽  
Type I ◽  
Type Ii ◽  
Finite Abelian Groups ◽  
Frobenius Theorem ◽  
Exact Counting

We find the number of compositions over finite abelian groups under two types of restrictions: (i) each part belongs to a given subset and (ii) small runs of consecutive parts must have given properties. Waring's problem over finite fields can be converted to type (i) compositions, whereas Carlitz and "locally Mullen" compositions can be formulated as type (ii) compositions. We use the multisection formula to translate the problem from integers to group elements, the transfer matrix method to do exact counting, and finally the Perron-Frobenius theorem to derive asymptotics. We also exhibit bijections involving certain restricted classes of compositions.

Type II codes over finite rings

2009 ◽  
Vol 53 (1) ◽  
pp. 203-212 ◽  
Author(s):  
Steven T. Dougherty ◽  
HongWei Liu
Keyword(s):  
Type Ii ◽  
Finite Rings ◽  
Type Ii Codes

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Sum-free subsets of finite abelian groups of type III

2016 ◽  
Vol 58 ◽  
pp. 181-202 ◽  
Author(s):  
R. Balasubramanian ◽  
Gyan Prakash ◽  
D.S. Ramana
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Type Iii
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