A generalized wreath product method for the enumeration of stereo and position isomers of polysubstituted organic compounds

Balasubramanian, K.

doi:10.1007/bf02399129

Cited by 98 publications

(37 citation statements)

References 13 publications

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“…And as is prototypical here, when the symmetry group of the underlying skeleton (on which substitutions are made) is comprised from a local part leaving units fixed (here carborane units) times a global part interchanging different units, a general theory is here formulated to facilitate the requisite constructions. This then extends some earlier 1 [9,10] similar theory for the special subcase when this symmetry group turns out to be a "wreath product". This yields what might be termed different types of isomer "sub-counts".…”

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confidence: 60%

“…Indeed this subgroup G fix must be normal, and there is a set {P x } of coset multipliers for G 0 in G fix . Then evidently T is the factor group of G fix in G. A special case of all this occurs when P is just the identity, and the result is what is called a "wreath" product, such as have been dealt with before (see footnote 1) [9] in the context of Pólya enumeration theory.…”

Section: Methodology For General Polycarboranesmentioning

confidence: 95%

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Enumeration of polycarborane isomers: especially dicarboranes

2012

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Various sorts of isomer enumeration problems are addressed in the context of polycarboranes, with special illustrative focus on the case of dicarboranes, for which then various numerical results are given. A systematic and general Pólya-theoretic methodology is used to make the computations, including some new techniques being applicable to a wide range of nano-structures built from a framework of like local subunits.

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confidence: 60%

Section: Methodology For General Polycarboranesmentioning

confidence: 95%

Enumeration of polycarborane isomers: especially dicarboranes

2012

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“…First, graphs play an important role in chemistry because they are used as representations of interactions, isomerization reactions, reaction pathways in chemical kinetics, NMR graphs,35 and molecules themselves. 36 Characteristic polynomials of graphs are important structural invariants, although they may not be unique, since they are invariant under different labelings of structures. These polynomials are generators for the number of ways dimers can be placed on tree lattices and thus play an important role in statistical mechanics.…”

Section: Introductionmentioning

confidence: 99%

Computer generation of the characteristic polynomials of chemical graphs

Balasubramanian

1984

J Comput Chem

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A computer program based on the Frame method for the characteristic polynomials of graphs is developed. This program makes use of an efficient polynomial algorithm of Frame for generating the coefficients in the characteristic polynomials of graphs. This program requires as input only the set of vertices that are neighbors of a given vertex and with labels smaller than the label of that vertex. The program generates and stores only the lower triangle of the adjacency matrix in canonical ordering in a one-dimensional array. The program is written in integer arithmetic, and it can be easily modified to real arithmetic. The coefficients in the characteristic polynomials of several graphs were generated in less than a few seconds, thus solving the difficult problem of generating characteristic polynomials of graphs. The characteristic polynomials of a number of very complicated graphs are obtained including for the first time the characteristic polynomial of an honeycomb lattice graph containing 54 vertices.

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“…The present author (13)(14)(15)(16)(17)(18)(19)(20)(21)(22) has been employing combinatorial and group theoretical techniques for problems in chemical physics. This paper uses a theorem of Williamson (23) recently generalized by Merris (24).…”

Section: Introductionmentioning

confidence: 99%

Computer generation of nuclear spin species and nuclear spin statistical weights

Balasubramanian¹

1982

J Comput Chem

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This article develops computer programs for computer generation of nuclear spin species and nuclear spin statistical weights of rovibronic levels. The programs developed here generate nuclear spin species and statistical weights from the group structures known as generalized character cycle indices (GCCIs) which are computed easily from the character table of the PI group of the molecule under consideration. Procedures are illustrated with examples.

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A generalized wreath product method for the enumeration of stereo and position isomers of polysubstituted organic compounds

Abstract: A generalized wreath product group is developed in the root-to-root product formalism for the enumeration of stereo and position isomers of polysubstituted organic compounds. The methods expounded here are used for enumerating the NMR signals of polysubstituted organic compounds.

Cited by 98 publications

References 13 publications

Enumeration of polycarborane isomers: especially dicarboranes

Enumeration of polycarborane isomers: especially dicarboranes

Computer generation of the characteristic polynomials of chemical graphs

Computer generation of nuclear spin species and nuclear spin statistical weights

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