Search results for "permuta"
showing 10 items of 171 documents
A new Euler–Mahonian constructive bijection
2011
AbstractUsing generating functions, MacMahon proved in 1916 the remarkable fact that the major index has the same distribution as the inversion number for multiset permutations, and in 1968 Foata gave a constructive bijection proving MacMahon’s result. Since then, many refinements have been derived, consisting of adding new constraints or new statistics.Here we give a new simple constructive bijection between the set of permutations with a given number of inversions and those with a given major index. We introduce a new statistic, mix, related to the Lehmer code, and using our new bijection we show that the bistatistic (mix,INV) is Euler–Mahonian. Finally, we introduce the McMahon code for …
A loopless algorithm for generating the permutations of a multiset
2003
AbstractMany combinatorial structures can be constructed from simpler components. For example, a permutation can be constructed from cycles, or a Motzkin word from a Dyck word and a combination. In this paper we present a constructor for combinatorial structures, called shuffle on trajectories (defined previously in a non-combinatorial context), and we show how this constructor enables us to obtain a new loopless generating algorithm for multiset permutations from similar results for simpler objects.
A fractal set from the binary reflected Gray code
2005
The permutation associated with the decimal expression of the binary reflected Gray code with $N$ bits is considered. Its cycle structure is studied. Considered as a set of points, its self-similarity is pointed out. As a fractal, it is shown to be the attractor of a IFS. For large values of $N$ the set is examined from the point of view of time series analysis
A note on the packing of two copies of some trees into their third power
2003
Abstract It is proved in [1] that if a tree T of order n is not a star, then there exists an edge-disjoint placement of two copies of this tree into its fourth power. In this paper, we prove the packing of some trees into their third power.
Analysis of properties of recombination operators proposed for the node-depth encoding
2011
The node-depth encoding is a representation for evolutionary algorithms applied to tree problems. Its represents trees by storing the nodes and their depth in a proper ordered list. The original formulation of the node-depth encoding has only mutation operators as the search mechanism. Although it is computationally efficient, the exclusive use of mutation restricts the exploration of the search space and the algorithm convergence. Then, this work proposes two specific recombination operators to improve the convergence of the algorithm using the node-depth encoding representation. These operators are based on recombination operators for permutation representations. Analysis of the proposed …
Improved constructions of mixed state quantum automata
2009
Quantum finite automata with mixed states are proved to be super-exponentially more concise rather than quantum finite automata with pure states. It was proved earlier by A. Ambainis and R. Freivalds that quantum finite automata with pure states can have an exponentially smaller number of states than deterministic finite automata recognizing the same language. There was an unpublished ''folk theorem'' proving that quantum finite automata with mixed states are no more super-exponentially more concise than deterministic finite automata. It was not known whether the super-exponential advantage of quantum automata is really achievable. We prove that there is an infinite sequence of distinct int…
Finite Soluble Groups with Permutable Subnormal Subgroups
2001
Abstract A finite group G is said to be a PST -group if every subnormal subgroup of G permutes with every Sylow subgroup of G . We shall discuss the normal structure of soluble PST -groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaining information about the global property. Moreover, a new approach to soluble PT -groups, i.e., soluble groups in which permutability is a transitive relation, follows naturally from our vision of PST -groups. Our techniques and results provide a unified point of view for T -groups, PT -groups, and PST -groups in the soluble universe, showing that the difference between these classes is…
Finitary Representations and Images of Transitive Finitary Permutation Groups
1999
Abstract We characterize the point stabilizers and kernels of finitary permutation representations of infinite transitive groups of finitary permutations. Moreover, the number of such representations is determined.
Large-scale network functional interactions during distraction and reappraisal in remitted bipolar and unipolar patients.
2017
Objectives The human brain is organized into large-scale networks that dynamically interact with each other. Extensive evidence has shown characteristic changes in certain large-scale networks during transitions from internally directed to externally directed attention. The aim of the present study was to compare these context-dependent network interactions during emotion regulation and to examine potential alterations in remitted unipolar and bipolar disorder patients. Methods We employed a multi-region generalized psychophysiological interactions analysis to quantify connectivity changes during distraction vs reappraisal pair-wise across 90 regions placed throughout the four networks of i…
A Note on Resampling the Integration Across the Correlation Integral with Alternative Ranges
2003
Abstract This paper reconsiders the nonlinearity test proposed by Ko[cbreve]enda (Ko[cbreve]enda, E. (2001). An alternative to the BDS test: integration across the correlation integral. Econometric Reviews20:337–351). When the analyzed series is non‐Gaussian, the empirical rejection rates can be much larger than the nominal size. In this context, the necessity of tabulating the empirical distribution of the statistic each time the test is computed is stressed. To that end, simple random permutation works reasonably well. This paper also shows, through Monte Carlo experiments, that Ko[cbreve]enda's test can be more powerful than the Brock et al. (Brock, W., Dechert, D., Scheickman, J., LeBar…