Search results for " permuta"
showing 10 items of 50 documents
Gray code for permutations with a fixed number of cycles
2007
AbstractWe give the first Gray code for the set of n-length permutations with a given number of cycles. In this code, each permutation is transformed into its successor by a product with a cycle of length three, which is optimal. If we represent each permutation by its transposition array then the obtained list still remains a Gray code and this allows us to construct a constant amortized time (CAT) algorithm for generating these codes. Also, Gray code and generating algorithm for n-length permutations with fixed number of left-to-right minima are discussed.
Lines on the Dwork pencil of quintic threefolds
2012
We present an explicit parametrization of the families of lines of the Dwork pencil of quintic threefolds. This gives rise to isomorphic curves which parametrize the lines. These curves are 125:1 covers of certain genus six curves. These genus six curves are first presented as curves in P^1*P^1 that have three nodes. It is natural to blow up P^1*P^1 in the three points corresponding to the nodes in order to produce smooth curves. The result of blowing up P^1*P^1 in three points is the quintic del Pezzo surface dP_5, whose automorphism group is the permutation group S_5, which is also a symmetry of the pair of genus six curves. The subgroup A_5, of even permutations, is an automorphism of ea…
From First Principles to the Burrows and Wheeler Transform and Beyond, via Combinatorial Optimization
2007
AbstractWe introduce a combinatorial optimization framework that naturally induces a class of optimal word permutations with respect to a suitably defined cost function taking into account various measures of relatedness between words. The Burrows and Wheeler transform (bwt) (cf. [M. Burrows, D. Wheeler, A block sorting lossless data compression algorithm, Technical Report 124, Digital Equipment Corporation, 1994]), and its analog for labelled trees (cf. [P. Ferragina, F. Luccio, G. Manzini, S. Muthukrishnan, Structuring labeled trees for optimal succinctness, and beyond, in: Proc. of the 45th Annual IEEE Symposium on Foundations of Computer Science, 2005, pp. 198–207]), are special cases i…
Combinatorial Gray codes for classes of pattern avoiding permutations
2007
The past decade has seen a flurry of research into pattern avoiding permutations but little of it is concerned with their exhaustive generation. Many applications call for exhaustive generation of permutations subject to various constraints or imposing a particular generating order. In this paper we present generating algorithms and combinatorial Gray codes for several families of pattern avoiding permutations. Among the families under consideration are those counted by Catalan, Schr\"oder, Pell, even index Fibonacci numbers and the central binomial coefficients. Consequently, this provides Gray codes for $\s_n(\tau)$ for all $\tau\in \s_3$ and the obtained Gray codes have distances 4 and 5.
Tetravalent single-chain avidin: from subunits to protein domains via circularly permuted avidins
2005
scAvd (single-chain avidin, where two dcAvd are joined in a single polypeptide chain), having four biotin-binding domains, was constructed by fusion of topologically modified avidin units. scAvd showed similar biotin binding and thermal stability properties as chicken avidin. The DNA construct encoding scAvd contains four circularly permuted avidin domains, plus short linkers connecting the four domains into a single polypeptide chain. In contrast with wild-type avidin, which contains four identical avidin monomers, scAvd enables each one of the four avidin domains to be independently modified by protein engineering. Therefore the scAvd scaffold can be used to construct spatially and stoich…
Avoiding patterns in irreducible permutations
2016
We explore the classical pattern avoidance question in the case of irreducible permutations, <i>i.e.</i>, those in which there is no index $i$ such that $\sigma (i+1) - \sigma (i)=1$. The problem is addressed completely in the case of avoiding one or two patterns of length three, and several well known sequences are encountered in the process, such as Catalan, Motzkin, Fibonacci, Tribonacci, Padovan and Binary numbers. Also, we present constructive bijections between the set of Motzkin paths of length $n-1$ and the sets of irreducible permutations of length $n$ (respectively fixed point free irreducible involutions of length $2n$) avoiding a pattern $\alpha$ for $\alpha \in \{13…
Some classes of finite groups and mutually permutable products
2008
[EN] This paper is devoted to the study of mutually permutable products of finite groups. A factorised group G=AB is said to be a mutually permutable product of its factors A and B when each factor permutes with every subgroup of the other factor. We prove that mutually permutable products of Y-groups (groups satisfying a converse of Lagrange's theorem) and SC-groups (groups whose chief factors are simple) are SC-groups, by means of a local version. Next we show that the product of pairwise mutually permutable Y-groups is supersoluble. Finally, we give a local version of the result stating that when a mutually permutable product of two groups is a PST-group (that is, a group in which every …
A generalization to Sylow permutability of pronormal subgroups of finite groups
2020
[EN] In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality.
CubeHarmonic: A new musical instrument based on Rubik{'}s cube with embedded motion sensor
2019
A contemporary challenge involves scientific education and the connection between new technologies and the heritage of the past. CubeHarmonic (CH) joins novelty and tradition, creativity and edu- cation, science and art. It takes shape as a novel musical instrument where magnetic 3D motion tracking technology meets musical per- formance and composition. CH is a Rubik’s cube with a note on each facet, and a chord or chord sequence on each face. The posi- tion of each facet is detected through magnetic 3D motion tracking. While scrambling the cube, the performer gets new chords and new chord sequences. CH can be used to compose, improvise,1 and teach music and mathematics (group theory, permu…
I vincoli della trasformazione: riflessioni sulla metamorfosi tra letteratura, filosofia e biologia
2019
Per sopravvivere gli esseri viventi sono costretto a modificarsi di continuo, adattandosi all’ambiente e al variare delle circostanze. In questa costante alterazione formale come si conciliano identità e mutamento? Come può l’individuo preservarsi dal totale dissolvimento in qualcos’altro? Questi sono solo alcuni dei quesiti che nei secoli hanno spinto studiosi di Morfologia, Estetica e Biologia a indagare le trasformazioni organiche. Nella presente trattazione cercheremo di chiarire le somiglianze e le differenze fra alcuni concetti chiave del vocabolario della metamorfosi (trasformazione, permutazione, vincolo, libertà di cambiamento, modularità organica) adottando un approccio multidisci…