Search results for "Permutation"
showing 10 items of 132 documents
Asymptotics for the standard and the Capelli identities
2003
Let {c n (St k )} and {c n (C k )} be the sequences of codimensions of the T-ideals generated by the standard polynomial of degreek and by thek-th Capelli polynomial, respectively. We study the asymptotic behaviour of these two sequences over a fieldF of characteristic zero. For the standard polynomial, among other results, we show that the following asymptotic equalities hold: $$\begin{gathered} c_n \left( {St_{2k} } \right) \simeq c_n \left( {C_{k^2 + 1} } \right) \simeq c_n \left( {M_k \left( F \right)} \right), \hfill \\ c_n \left( {St_{2k + 1} } \right) \simeq c_n \left( {M_{k \times 2k} \left( F \right) \oplus M_{2k \times k} \left( F \right)} \right), \hfill \\ \end{gathered} $$ wher…
Der Satz von Tits für PGL2(R), R ein kommutativer Ring vom stabilen Rang 2
1996
Certain permutation groups on sets with distance relation are characterized as groups of projectivities PGL2(R) on the projective line over a commutative ring R of stable rank 2, thus generalizing a classical result of Tits where R is a field.
Quantum Queries on Permutations
2015
K. Iwama and R. Freivalds considered query algorithms where the black box contains a permutation. Since then several authors have compared quantum and deterministic query algorithms for permutations. It turns out that the case of \(n\)-permutations where \(n\) is an odd number is difficult. There was no example of a permutation problem where quantization can save half of the queries for \((2m+1)\)-permutations if \(m\ge 2\). Even for \((2m)\)-permutations with \(m\ge 2\), the best proved advantage of quantum query algorithms is the result by Iwama/Freivalds where the quantum query complexity is \(m\) but the deterministic query complexity is \((2m-1)\). We present a group of \(5\)-permutati…
The Structure Group and the Permutation Group of a Set-Theoretic Solution of the Quantum Yang–Baxter Equation
2021
We describe the left brace structure of the structure group and the permutation group associated to an involutive, non-degenerate set-theoretic solution of the quantum YangBaxter equation by using the Cayley graph of its permutation group with respect to its natural generating system. We use our descriptions of the additions in both braces to obtain new properties of the structure and the permutation groups and to recover some known properties of these groups in a more transparent way.
Transitive permutation groups in which all derangements are involutions
2006
AbstractLet G be a transitive permutation group in which all derangements are involutions. We prove that G is either an elementary abelian 2-group or is a Frobenius group having an elementary abelian 2-group as kernel. We also consider the analogous problem for abstract groups, and we classify groups G with a proper subgroup H such that every element of G not conjugate to an element of H is an involution.
On permutations of class sums of alternating groups
1997
We prove a result concerning the class sums of the alternating group An; as a consequence we deduce that if θ is a normalized automorphism of the integral group ring then there exists such that is the identity on , where Sn:is the symmetric group and is the center of
Longest Motifs with a Functionally Equivalent Central Block
2004
International audience; This paper presents a generalization of the notion of longest repeats with a block of k don't care symbols introduced by [Crochemore et al., LATIN 2004] (for k fixed) to longest motifs composed of three parts: a first and last that parameterize match (that is, match via some symbol renaming, initially unknown), and a functionally equivalent central block. Such three-part motifs are called longest block motifs. Different types of functional equivalence, and thus of matching criteria for the central block are considered, which include as a subcase the one treated in [Crochemore et al., LATIN 2004] and extend to the case of regular expressions with no Kleene closure or …
On fixed points of the Burrows-Wheeler transform
2017
The Burrows-Wheeler Transform is a well known transformation widely used in Data Compression: important competitive compression software, such as Bzip (cf. [1]) and Szip (cf. [2]) and some indexing software, like the FM-index (cf. [3]), are deeply based on the Burrows Wheeler Transform. The main advantage of using BWT for data compression consists in its feature of "clustering" together equal characters. In this paper we show the existence of fixed points of BWT, i.e., words on which BWT has no effect. We show a characterization of the permutations associated to BWT of fixed points and we give the explicit form of fixed points on a binary ordered alphabet a, b having at most four b's and th…
Divisible designs from semifield planes
2002
AbstractWe give a general method to construct divisible designs from semifield planes and we use this technique to construct some divisible designs. In particular, we give the case of twisted field plane as an example.
A bijection between words and multisets of necklaces
2012
Two of the present authors have given in 1993 a bijection Phi between words on a totally ordered alphabet and multisets of primitive necklaces. At the same time and independently, Burrows and Wheeler gave a data compression algorithm which turns out to be a particular case of the inverse of Phi. In the present article, we show that if one replaces in Phi the standard permutation of a word by the co-standard one (reading the word from right to left), then the inverse bijection is computed using the alternate lexicographic order (which is the order of real numbers given by continued fractions) on necklaces, instead of the lexicographic order as for Phi(-1). The image of the new bijection, ins…