Double Occurrence Words: Their Graphs and Matrices

Guterman, Alexander; Kreines, E. M.; Ostroukhova, N. V.

doi:10.1007/s10958-020-04928-5

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Definition 3 ([6]1

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2022

2023

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Cited by 3 publications

(1 citation statement)

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“…Subsequently, Burns et al referred to the double-occurrence word as an assembly word in which every symbol appears exactly twice [7]. The definition of assembly word is given in [8] as follows.…”

Section: Definition 3 ([6]mentioning

confidence: 99%

Tangled Cord of FTTM4

et al. 2023

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Fuzzy Topological Topographic Mapping (FTTM) is a mathematical model that consists of a set of homeomorphic topological spaces designed to solve the neuro magnetic inverse problem. A sequence of FTTM, denoted as FTTMn, is an extension of FTTM that is arranged in a symmetrical form. The special characteristic of FTTM, namely the homeomorphisms between its components, allows the generation of new FTTM. Later, the FTTMn can also be viewed as a graph. Previously, a group of researchers defined an assembly graph and utilized it to model a DNA recombination process. Some researchers then used this to introduce the concept of tangled cords for assembly graphs. In this paper, the tangled cord for FTTM4 is used to calculate the Eulerian paths. Furthermore, it is utilized to determine the least upper bound of the Hamiltonian paths of its assembly graph. Hence, this study verifies the conjecture made by Burns et al.

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Section: Definition 3 ([6]mentioning

confidence: 99%