Cyclic permutation ≈ Cyclic permutation
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Random Permutation Set Open
For exploring the meaning of the power set in evidence theory, a possible explanation of power set is proposed from the view of Pascal’s triangle and combinatorial number. Here comes the question: what would happen if the combinatorial num…
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Permutation-equivariant neural networks applied to dynamics prediction Open
The introduction of convolutional layers greatly advanced the performance of neural networks on image tasks due to innately capturing a way of encoding and learning translation-invariant operations, matching one of the underlying symmetrie…
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An algorithm for generating permutation algebras using soft spaces Open
Soft set theory has recently gained significance for finding rational and logical solutions to various real-life problems, which involve uncertainty, impreciseness and vagueness. In this paper, we introduced an algorithm to find permutatio…
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Fixed points and cycle structure of random permutations Open
Using the recently developed notion of permutation limits this paper derives the limiting distribution of the number of fixed points and cycle structure for any convergent sequence of random permutations, under mild regularity conditions. …
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Existence of solutions for tripled system of fractional differential equations involving cyclic permutation boundary conditions Open
In this paper, we introduce and study a tripled system of three associated fractional differential equations. Prior to proceeding to the main results, the proposed system is converted into an equivalent integral form by the help of fractio…
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Permutation Entropy Based on Non-Uniform Embedding Open
A novel visualization scheme for permutation entropy is presented in this paper. The proposed scheme is based on non-uniform attractor embedding of the investigated time series. A single digital image of permutation entropy is produced by …
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Cyclic permutations in determining crossing numbers Open
The crossing number of a graph G is the minimum number of edge crossings over all drawings of G in the plane. Recently, the crossing numbers of join products of two graphs have been studied. In the paper, we extend know results concerning …
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Finding Compositional Inverses of Permutations From the AGW Criterion Open
Permutation polynomials and their compositional inverses have wide applications in cryptography, coding theory, and combinatorial designs. Motivated by several previous results on finding compositional inverses of permutation polynomials o…
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New Permutation Trinomials Constructed from Fractional Polynomials Open
Permutation trinomials over finite fields consititute an active research due to their simple algebraic form, additional extraordinary properties and their wide applications in many areas of science and engineering. In the present paper, si…
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Permutation Tests Using Arbitrary Permutation Distributions Open
Permutation tests date back nearly a century to Fisher’s randomized experiments, and remain an immensely popular statistical tool, used for testing hypotheses of independence between variables and other common inferential questions. Much o…
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Cocyclic solutions to the Yang-Baxter equation Open
The systematic study of involutive non-degenerate set-theoretic solutions to the Yang-Baxter equation was initiated by Etingof et al. (Duke Math. J., 1999), who introduced the structure group of a solution and its retraction, the permutati…
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Homogeneous 3-Dimensional Permutation Structures Open
We provide a classification of the homogeneous 3-dimensional permutation structures, i.e. homogeneous structures in a language of 3 linear orders, partially answering a 2002 question of Cameron. We also arrive at a natural description of a…
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On intersection density of transitive groups of degree a product of two odd primes Open
Two elements $g$ and $h$ of a permutation group $G$ acting on a set $V$ are said to be intersecting if $g(v) = h(v)$ for some $v \in V$. More generally, a subset ${\cal F}$ of $G$ is an intersecting set if every pair of elements of ${\cal …
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( <i>n</i> , <i>n</i> ( <i>n</i> ‐1), <i>n</i> ‐1) Permutation group codes Open
Two different subgroups C n and L n of symmetric group S n are first designed and then to construct a family of permutation group codes P n with code length n , minimum Hamming distance n − 1, cardinality n ( n − 1) and error‐correcting ca…
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Erdős-Ko-Rado problems for permutation groups Open
In this paper, we study intersecting sets in primitive and quasiprimitive permutation groups. Let $G \leqslant \mathrm{Sym}(Ω)$ be a transitive permutation group, and ${S}$ an intersecting set. Previous results show that if $G$ is either 2…
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Erd\H{o}s-Ko-Rado problems for permutation groups Open
In this paper, we study intersecting sets in primitive and quasiprimitive\npermutation groups. Let $G \\leqslant \\mathrm{Sym}(\\Omega)$ be a transitive\npermutation group, and ${S}$ an intersecting set. Previous results show that if\n$G$ …
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On signed Young permutation modules and signed <i>p</i>-Kostka numbers Open
We prove the existence and main properties of signed Young modules for the symmetric group, using only basic facts about symmetric group representations and the Broué correspondence. We then prove new reduction theorems for the signed p -K…
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Further results on permutation polynomials and complete permutation polynomials over finite fields Open
In this paper, by employing the AGW criterion and determining the number of solutions to some equations over finite fields, we further investigate nine classes of permutation polynomials over $ \mathbb{F}_{p^n} $ with the form $ (x^{p^m}-x…
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Universality of random permutations Open
It is a classical fact that for any $\varepsilon > 0$, a random permutation of length $n = (1 + \varepsilon) k^2 / 4$ typically contains a monotone subsequence of length $k$. As a far-reaching generalization, Alon conjectured that a random…
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Lorentz- and permutation-invariants of particles Open
Two theorems of Weyl tell us that the algebra of Lorentz- (and parity-) invariant polynomials in the momenta of n particles are generated by the dot products and that the redundancies which arise when n exceeds the spacetime dimension d ar…
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Hamming Graphs and Permutation Codes Open
A permutation code can be represented as a graph, in which the nodes correspond to the permutation codewords and the weights on the edges are the Hamming distances between the codewords. Graphs belonging to this class are called permutatio…
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Intersecting principal Bruhat ideals and grades of simple modules Open
prove that the grades of simple modules indexed by boolean permutations, over the incidence algebra of the symmetric group with respect to the Bruhat order, are given by Lusztig's a-function. Our arguments are combinatorial, and include a …
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The Cycle Polynomial of a Permutation Group Open
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 $\Omega$. …
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Kaleidoscopic groups: permutation groups constructed from dendrite homeomorphisms Open
Given a transitive permutation group, a fundamental object for studying its higher transitivity properties is the permutation action of its isotropy subgroup. We reverse this relationship and introduce a universal construction of infinite …
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The classification of 3 2-transitive permutation groups and 1 2-transitive linear groups Open
A linear group , where is a finite vector space, is called -transitive if all the -orbits on the set of nonzero vectors have the same size. We complete the classification of all the -transitive linear groups. As a consequence we complete …
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Primitive permutation IBIS groups Open
Let G be a finite permutation group on Ω. An ordered sequence of elements of Ω, (ω1,...,ωt), is an irredundant base for G if the pointwise stabilizer G(ωjavax.xml.bind.JAXBElement@606ca359,...,ωjavax.xml.bind.JAXBElement@77e0dd48) is trivi…
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Doubly stochastic matrices and the Bruhat order Open
The Bruhat order is defined in terms of an interchange operation on the set of permutation matrices of order n which corresponds to the transposition of a pair of elements in a permutation. We introduce an extension of this partial order, …
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Sharply 2-transitive groups of finite Morley rank Open
A sharply 2-transitive permutation group of finite Morley rank and characteristic 2 splits; a split sharply 2-transitive permutation group of finite Morley rank and characteristic different from 2 is the group of affine transformations of …
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Permutation Pattern matching in (213, 231)-avoiding permutations Open
Given permutations σ of size k and π of size n with k < n, the permutation pattern matching problem is to decide whether σ occurs in π as an order-isomorphic subsequence. We give a linear-time algorithm in case both π and σ avoid the two s…
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Cyclic Permutation Groups that are Automorphism Groups of Graphs Open
In this paper we establish conditions for a permutation group generated by a single permutation to be an automorphism group of a graph. This solves the so called concrete version of König’s problem for the case of cyclic groups. We establi…