69,744 research outputs found
On uniquely k-determined permutations
There are several approaches to study occurrences of consecutive patterns in
permutations such as the inclusion-exclusion method, the tree representations
of permutations, the spectral approach and others. We propose yet another
approach to study occurrences of consecutive patterns in permutations. The
approach is based on considering the graph of patterns overlaps, which is a
certain subgraph of the de Bruijn graph.
While applying our approach, the notion of a uniquely -determined
permutation appears. We give two criteria for a permutation to be uniquely
-determined: one in terms of the distance between two consecutive elements
in a permutation, and the other one in terms of directed hamiltonian paths in
the certain graphs called path-schemes. Moreover, we describe a finite set of
prohibitions that gives the set of uniquely -determined permutations. Those
prohibitions make applying the transfer matrix method possible for determining
the number of uniquely -determined permutations.Comment: 12 page
Photon echo quantum RAM integration in quantum computer
We have analyzed an efficient integration of the multi-qubit echo quantum
memory into the quantum computer scheme on the atomic resonant ensembles in
quantum electrodynamics cavity. Here, one atomic ensemble with controllable
inhomogeneous broadening is used for the quantum memory node and other atomic
ensembles characterized by the homogeneous broadening of the resonant line are
used as processing nodes. We have found optimal conditions for efficient
integration of multi-qubit quantum memory modified for this analyzed physical
scheme and we have determined a specified shape of the self temporal modes
providing a perfect reversible transfer of the photon qubits between the
quantum memory node and arbitrary processing nodes. The obtained results open
the way for realization of full-scale solid state quantum computing based on
using the efficient multi-qubit quantum memory.Comment: 13 pages, 5 figure
Klein Topological Field Theories from Group Representations
We show that any complex (respectively real) representation of finite group
naturally generates a open-closed (respectively Klein) topological field theory
over complex numbers. We relate the 1-point correlator for the projective plane
in this theory with the Frobenius-Schur indicator on the representation. We
relate any complex simple Klein TFT to a real division ring
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