An application to combinatorics: The theory of enumeration under group action

1975 ◽  
pp. 103-166
Author(s):  
Adalbert Kerber
Keyword(s):  
Group Action ◽  
Enumeration Under Group Action

Enumeration Under Group Action

2018 ◽  
pp. 75-101
Author(s):  
Richard P. Stanley
Keyword(s):  
Group Action ◽  
Enumeration Under Group Action

scholarly journals Enumeration under group action

Combinatorics ◽  
1994 ◽  
pp. 245-256
Keyword(s):  
Group Action ◽  
Enumeration Under Group Action

Enumeration under Group Action

2009 ◽  
pp. 72-85
Author(s):  
Sebastian M. Cioabă ◽  
M. Ram Murty
Keyword(s):  
Group Action ◽  
Enumeration Under Group Action

Enumeration Under Group Action

2013 ◽  
pp. 75-101
Author(s):  
Richard P. Stanley
Keyword(s):  
Group Action ◽  
Enumeration Under Group Action

On the family of Riemann surfaces with tetrahedral group action

2019 ◽  
Vol 42 (3) ◽  
pp. 476-495
Author(s):  
Ryota Hirakawa
Keyword(s):  
Group Action ◽  
Riemann Surfaces ◽  
The Family

scholarly journals Optimized CSIDH Implementation Using a 2-Torsion Point

Cryptography ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 20 ◽  
Author(s):  
Donghoe Heo ◽  
Suhri Kim ◽  
Kisoon Yoon ◽  
Young-Ho Park ◽  
Seokhie Hong
Keyword(s):  
Elliptic Curve ◽  
Group Action ◽  
Large Degree ◽  
Transitive Group ◽  
Optimization Method ◽  
Torsion Point ◽  
Torsion Points ◽  
Diffie Hellman ◽  
Odd Degree ◽  
Montgomery Curve

The implementation of isogeny-based cryptography mainly use Montgomery curves, as they offer fast elliptic curve arithmetic and isogeny computation. However, although Montgomery curves have efficient 3- and 4-isogeny formula, it becomes inefficient when recovering the coefficient of the image curve for large degree isogenies. Because the Commutative Supersingular Isogeny Diffie-Hellman (CSIDH) requires odd-degree isogenies up to at least 587, this inefficiency is the main bottleneck of using a Montgomery curve for CSIDH. In this paper, we present a new optimization method for faster CSIDH protocols entirely on Montgomery curves. To this end, we present a new parameter for CSIDH, in which the three rational two-torsion points exist. By using the proposed parameters, the CSIDH moves around the surface. The curve coefficient of the image curve can be recovered by a two-torsion point. We also proved that the CSIDH while using the proposed parameter guarantees a free and transitive group action. Additionally, we present the implementation result using our method. We demonstrated that our method is 6.4% faster than the original CSIDH. Our works show that quite higher performance of CSIDH is achieved while only using Montgomery curves.

scholarly journals On the automorphism group of a symplectic half-flat 6-manifold

2019 ◽  
Vol 31 (1) ◽  
pp. 265-273
Author(s):  
Fabio Podestà ◽  
Alberto Raffero
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Group Action ◽  
Cohomogeneity One ◽  
Cohomogeneity One Action

Abstract We prove that the automorphism group of a compact 6-manifold M endowed with a symplectic half-flat {\mathrm{SU}(3)} -structure has Abelian Lie algebra with dimension bounded by {\min\{5,b_{1}(M)\}} . Moreover, we study the properties of the automorphism group action and we discuss relevant examples. In particular, we provide new complete examples on {T\mathbb{S}^{3}} which are invariant under a cohomogeneity one action of {\mathrm{SO}(4)} .

scholarly journals Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities

2021 ◽  
Vol 385 ◽  
pp. 107793
Author(s):  
Dinakar Muthiah
Keyword(s):  
Weyl Group ◽  
Group Action

Group Action in the Baltic States

1997 ◽  
Vol 20 (3) ◽  
pp. 353-370 ◽  
Author(s):  
Klaus Viitanen
Keyword(s):  
Group Action ◽  
Baltic States ◽  
The Baltic
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