HAMILTONICITY PROPERTIES OF CIRCULANT DIGRAPHS OF SEMIPRIME OR POWER OF PRIME ORDER

2017 ◽  
Vol 101 (11) ◽  
pp. 2461-2474
Author(s):  
Zbigniew R. Bogdanowicz
Keyword(s):  
Prime Order ◽  
Circulant Digraphs

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption

Infinite Circulant Digraphs and Random Infinite Circulant Digraphs

2002 ◽  
Vol 18 (4) ◽  
pp. 817-822 ◽  
Author(s):  
Qiang Xiang Huang ◽  
Ji Xiang Meng ◽  
Fu Ji Zhang
Keyword(s):  
Circulant Digraphs

scholarly journals Gaussian integral circulant digraphs

2011 ◽  
Vol 311 (1) ◽  
pp. 45-50 ◽  
Author(s):  
Ying Xu ◽  
Jixiang Meng
Keyword(s):  
Gaussian Integral ◽  
Circulant Digraphs

scholarly journals Atomic Latin Squares based on Cyclotomic Orthomorphisms

10.37236/1919 ◽  
2005 ◽  
Vol 12 (1) ◽  
Author(s):  
Ian M. Wanless
Keyword(s):  
Finite Fields ◽  
Complete Graph ◽  
Prime Order ◽  
Automorphism Groups ◽  
Latin Square ◽  
Latin Squares ◽  
Established Method ◽  
Cyclic Groups ◽  
Complete Bipartite Graphs ◽  
First Time

Atomic latin squares have indivisible structure which mimics that of the cyclic groups of prime order. They are related to perfect $1$-factorisations of complete bipartite graphs. Only one example of an atomic latin square of a composite order (namely 27) was previously known. We show that this one example can be generated by an established method of constructing latin squares using cyclotomic orthomorphisms in finite fields. The same method is used in this paper to construct atomic latin squares of composite orders 25, 49, 121, 125, 289, 361, 625, 841, 1369, 1849, 2809, 4489, 24649 and 39601. It is also used to construct many new atomic latin squares of prime order and perfect $1$-factorisations of the complete graph $K_{q+1}$ for many prime powers $q$. As a result, existence of such a factorisation is shown for the first time for $q$ in $\big\{$529, 2809, 4489, 6889, 11449, 11881, 15625, 22201, 24389, 24649, 26569, 29929, 32041, 38809, 44521, 50653, 51529, 52441, 63001, 72361, 76729, 78125, 79507, 103823, 148877, 161051, 205379, 226981, 300763, 357911, 371293, 493039, 571787$\big\}$. We show that latin squares built by the 'orthomorphism method' have large automorphism groups and we discuss conditions under which different orthomorphisms produce isomorphic latin squares. We also introduce an invariant called the train of a latin square, which proves to be useful for distinguishing non-isomorphic examples.

scholarly journals Euler’s criterion for prime order in the PID case

2020 ◽  
Vol 192 (3) ◽  
pp. 259-265
Author(s):  
Jagmohan Tanti
Keyword(s):  
Prime Order

scholarly journals Weights of Partitions and Character Zeros

10.37236/1862 ◽  
2004 ◽  
Vol 11 (2) ◽  
Author(s):  
Christine Bessenrodt ◽  
Jørn B. Olsson
Keyword(s):  
Irreducible Character ◽  
Prime Order ◽  
Alternating Groups ◽  
Non Linear

We classify partitions which are of maximal $p$-weight for all odd primes $p$. As a consequence, we show that any non-linear irreducible character of the symmetric and alternating groups vanishes on some element of prime order.

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