2021
DOI: 10.3390/sym13101850
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Symmetry, Combinatorics, Artificial Intelligence, Music and Spectroscopy

Abstract: Symmetry forms the foundation of combinatorial theories and algorithms of enumeration such as Möbius inversion, Euler totient functions, and the celebrated Pólya’s theory of enumeration under the symmetric group action. As machine learning and artificial intelligence techniques play increasingly important roles in the machine perception of music to image processing that are central to many disciplines, combinatorics, graph theory, and symmetry act as powerful bridges to the developments of algorithms for such … Show more

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Cited by 13 publications
(5 citation statements)
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“…For the sake of demonstration, we consider the hyperfine structures arising from the coupling of the unpaired electron with 13 C nuclear spins in the three TM-MOFs considered here. The combinatorial method to generate the ESR hyperfine patterns from the nuclear equivalence classes involves generating function methods 56,57 which have been well described in the cited references in extensive details. Hence we shall not repeat the extensive formalisms here.…”
Section: Resultsmentioning
confidence: 99%
“…For the sake of demonstration, we consider the hyperfine structures arising from the coupling of the unpaired electron with 13 C nuclear spins in the three TM-MOFs considered here. The combinatorial method to generate the ESR hyperfine patterns from the nuclear equivalence classes involves generating function methods 56,57 which have been well described in the cited references in extensive details. Hence we shall not repeat the extensive formalisms here.…”
Section: Resultsmentioning
confidence: 99%
“…Although this is an important measure of aromaticity, it is a difficult quantity to deal with as the matching spectra of graphs containing a large number of vertices with several fused cycles as in polycyclic aromatic compounds are difficult to obtain, although the graph spectra can be more readily obtained by diagonalizing the adjacency matrix by invoking symmetry or by the standard Givens-Householder tri-diagonalization technique. Even for graphs containing a very large number of vertices, it has been shown that the Hadamard transform technique can be employed to extract all eigenvalues of the adjacency matrix [80].…”
Section: Delta Polynomials: Mathematical and Computational Methodsmentioning
confidence: 99%
“…As technology for simulating, extending, and expanding human intelligence, artificial intelligence has been advanced from the primary form of computational intelligence to the advanced form of perceptual intelligence and cognitive intelligence [19][20][21][22]. Music is one of the reappearance forms of human emotion and cognition, and artificial intelligence technology has gradually penetrated into every link of music diffusion.…”
Section: Artificial Intelligence and Musicmentioning
confidence: 99%