The character table of a sharply 5-transitive subgroup of the alternating group of degree 12 [PDF]
International Journal of Group Theory, 2021 We calculate the character table of a sharply $5$-transitive subgroup of $\alter(12)$, and of a sharply $4$-transitive subgroup of $\alter(11)$. Our presentation of these calculations is new because we make no reference to the sporadic simple Mathieu
Nick Gill, Sam Hughes
doaj +1 more source
Near-Optimal Performance Bounds for Orthogonal and Permutation Group Synchronization via Spectral Methods [PDF]
Applied and Computational Harmonic Analysis, 2020 Group synchronization asks to recover group elements from their pairwise measurements. It has found numerous applications across various scientific disciplines.
Shuyang Ling
semanticscholar +1 more source
ON THE HEIGHT AND RELATIONAL COMPLEXITY OF A FINITE PERMUTATION GROUP [PDF]
Nagoya mathematical journal, 2020 Let G be a permutation group on a set $\Omega $ of size t. We say that $\Lambda \subseteq \Omega $ is an independent set if its pointwise stabilizer is not equal to the pointwise stabilizer of any proper subset of $\Lambda $ .
Nick Gill, Bianca Lod'a, Pablo Spiga
semanticscholar +1 more source
Indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level 2 with abelian permutation group [PDF]
Forum mathematicum, 2020 We present a construction of all finite indecomposable involutive solutions of the Yang–Baxter equation of multipermutational level at most 2 with abelian permutation group.
P. Jedlička +2 more
semanticscholar +1 more source
Theoretical guarantees for permutation-equivariant quantum neural networks [PDF]
npj Quantum Information, 2022 Despite the great promise of quantum machine learning models, there are several challenges one must overcome before unlocking their full potential. For instance, models based on quantum neural networks (QNNs) can suffer from excessive local minima and ...
Louis Schatzki +3 more
semanticscholar +1 more source
Cubic Cayley graphs with small diameter. [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 In this paper we apply Polya's Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group.
Eugene Curtin
doaj +3 more sources
Computing Minimal Generating Sets of Invariant Rings of Permutation Groups with SAGBI-Gröbner Basis [PDF]
Discrete Mathematics & Theoretical Computer Science, 2001 We present a characteristic-free algorithm for computing minimal generating sets of invariant rings of permutation groups. We circumvent the main weaknesses of the usual approaches (using classical Gröbner basis inside the full polynomial ring, or pure ...
Nicolas Thiéry
doaj +1 more source
Application of a permutation group on sasirangan pattern
Desimal, 2021 A permutation group is a group of all permutations of some set. If the set that forms a permutation group is the n-first of natural number, then a permutation group is called a symmetry group.
Na'imah Hijriati +3 more
doaj +1 more source
On the Saxl graph of a permutation group [PDF]
Mathematical Proceedings of the Cambridge Philosophical Society, 2017 Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its pointwise stabiliser in G is trivial. In this paper we introduce and study an associated graph Σ(G), which we call the Saxl graph of G. The vertices of Σ(G) are the points of Ω,
Timothy C. Burness, Michael Giudici
semanticscholar +1 more source
The Cycle Polynomial of a Permutation Group [PDF]
Electronic Journal of Combinatorics, 2017 The cycle polynomial of a finite permutation group $G$ is the generating function for the number of elements of $G$ with a given number of cycles: \[F_G(x) = \sum_{g\in G}x^{c(g)},\] where $c(g)$ is the number of cycles of $g$ on $\Omega$.
P. Cameron, Jason Semeraro
semanticscholar +1 more source