Systematic Enumeration of Ferrocene Derivatives by Unit-Subduced-Cycle-Index Method and Characteristic-Monomial Method

1999 ◽  
Vol 72 (11) ◽  
pp. 2409-2416 ◽  
Author(s):  
Shinsaku Fujita
Keyword(s):  
Ferrocene Derivatives ◽  
Cycle Index ◽  
Index Method ◽  
Systematic Enumeration ◽  
Unit Subduced Cycle Index

scholarly journals Application of GAP (groups, algorithms and programming) system to stereoisograms for characterizing RS-stereoisomers of cubane derivatives

2021 ◽  
Vol 87 (2) ◽  
pp. 207-270
Author(s):  
Shinsaku Fujita ◽  
Keyword(s):  
Permutation Group ◽  
Point Group ◽  
Gap Functions ◽  
Programming System ◽  
Cycle Index ◽  
Index Method ◽  
Type V ◽  
Partial Cycle

The PCI (Partial-Cycle-Index) method of Fujita’s USCI (Unit-Subduced-CycleIndex) approach has been applied to symmetry-itemized enumerations of cubane derivatives, where groups for specifying three-aspects of symmetry, i.e., the point group for chirality/achirality, the RS-stereogenic group for RS-stereogenicity/RS-astereogenicity, and the LR-permutation group for sclerality/ascrelarity are considered as the subgroups of the RS-stereoisomeric group . Five types of stereoisograms are adopted as diagrammatical expressions of , after combined-permutation representations (CPR) are created as new tools for treating various groups according to Fujita’s stereoisogram approach. The use of CPRs under the GAP (Groups, Algorithms and Programming) system has provided new GAP functions for promoting symmetry-itemized enumerations. The type indices for characterizing stereoisograms (e.g., for a type-V stereoisogram) have been sophisticated into RS-stereoisomeric indices (e.g., for a cubane derivative with the composition ). The type-V stereoisograms for cubane derivatives with the composition are discussed under extended pseudoasymmetry as a new concept.

scholarly journals Standard mark table and standard USCI-CF table of the point group D6h. Unification of candidates derived from different D6h-skeletons

2021 ◽  
Vol 87 (3) ◽  
pp. 481-525
Author(s):  
Shinsaku Fujita ◽  
Keyword(s):  
Point Group ◽  
Gap Function ◽  
Combinatorial Enumeration ◽  
Cycle Index ◽  
Single Standard ◽  
Partial Cycle ◽  
Unit Subduced Cycle Index ◽  
Chirality Fittingness ◽  
Usci Approach ◽  
Cycle Indices

Combined-permutation representations (CPRs) for characterizing -skeletons (a benzene skeleton, a Haworth-projected skeleton, a superphane skeleton, and a coronene skeleton) are constructed by starting from respective sets of generators, where the permutation of each generator is combined with a mirror-permutation of 2-cycle to treat both achiral and chiral substituents under the GAP system. Thereby, the CPR of degree 8 (= 6 + 2) for the benzene skeleton, the CPR of degree 14 (= 12 + 2) for the Haworth-projected skeleton, the CPR of degree 14 (= 12 + 2) for the superphane skeleton, the CPR of degree 14 (= 12 + 2) for the coronene skeleton are generated to give primary mark tables (tables of marks) based on these CPRs. These primary mark tables generated by the GAP system are different in the sequence of subgroups from each other, although they stem from the same point group . They are unified into a single standard mark table by means of a newly-devised GAP function MarkTableforUSCI. Moreover, another newly-devised GAP function constructUSCITable is employed to construct a standard USCI-CF (unit-subduced-cycle-index-with-chirality-fittingness) table concordantly. After a set of PCI-CFs (partial cycle indices with chirality fittingness) is calculated for each skeleton, symmetry-itemized combinatorial enumeration is conducted by means of the PCI method of Fujita’s USCI approach (S. Fujita, Symmetry and Combinatorial Enumeration in Chemistry, Springer-Verlag, Berlin-Heidelberg, 1991).

scholarly journals Enumeration of Unlabeled Directed Hypergraphs

10.37236/2766 ◽  
2013 ◽  
Vol 20 (1) ◽  
Author(s):  
Jianguo Qian
Keyword(s):  
Permutation Group ◽  
Equivalence Class ◽  
Directed Graphs ◽  
Disjoint Cycle ◽  
Cycle Decomposition ◽  
Cycle Index ◽  
Index Method ◽  
Directed Hypergraphs ◽  
Counting Lemma

We consider the enumeration of unlabeled directed hypergraphs by using Pólya's counting theory and Burnside's counting lemma. Instead of characterizing the cycle index of the permutation group acting on the hyperarc set $A$, we treat each cycle in the disjoint cycle decomposition of a permutation $\rho$ acting on $A$ as an equivalence class (or orbit) of $A$ under the operation of the group generated by $\rho$. Compared to the cycle index method, our approach is  more effective in  dealing with the enumeration of directed hypergraphs. We deduce the explicit counting formulae for the unlabeled $q$-uniform and unlabeled general directed hypergraphs. The former generalizes the well known result for 2-uniform directed hypergraphs, i.e., for the ordinary directed graphs introduced by Harary and Palmer.

scholarly journals The Fujita combinatorial enumeration for the non-rigid group of 2,4-dimethylbenzene

2010 ◽  
Vol 75 (1) ◽  
pp. 91-99 ◽  
Author(s):  
Ali Moghani ◽  
Naghdi Sedeh ◽  
Reza Sorouhesh
Keyword(s):  
Group Theory ◽  
Cyclic Group ◽  
Wreath Products ◽  
Combinatorial Enumeration ◽  
Cycle Index ◽  
Dominant Classes ◽  
First Time ◽  
Unit Subduced Cycle Index ◽  
Rigid Group

Using non-rigid group theory, it was previously shown that the full non-rigid group of 2,4-dimethylbenzene is an ummatured and isomorphic to the group C2?(C3wrC2) of order 36, where Cn is the cyclic group of order n, the symbols ? and wr stand for the direct and wreath products, respectively. Herein, it is first shown that this group has 12 dominant classes. Then, the Markaracter Table, the Table of all integer-valued characters and the unit subduced cycle index (USCI) Table of the full non-rigid group of 2,4-dimethylbenzene are successfully derived for the first time.

Detecting Random Responses in a Personality Scale Using IRT-Based Person-Fit Indices

2019 ◽  
Vol 35 (1) ◽  
pp. 126-136 ◽  
Author(s):  
Tour Liu ◽  
Tian Lan ◽  
Tao Xin
Keyword(s):  
Experimental System ◽  
Real Data ◽  
Fit Indices ◽  
Random Response ◽  
Person Fit ◽  
Index Method ◽  
Single Person ◽  
Person Fit Index ◽  
Random Responses ◽  
Response Behaviors

Abstract. Random response is a very common aberrant response behavior in personality tests and may negatively affect the reliability, validity, or other analytical aspects of psychological assessment. Typically, researchers use a single person-fit index to identify random responses. This study recommends a three-step person-fit analysis procedure. Unlike the typical single person-fit methods, the three-step procedure identifies both global misfit and local misfit individuals using different person-fit indices. This procedure was able to identify more local misfit individuals than single-index method, and a graphical method was used to visualize those particular items in which random response behaviors appear. This method may be useful to researchers in that it will provide them with more information about response behaviors, allowing better evaluation of scale administration and development of more plausible explanations. Real data were used in this study instead of simulation data. In order to create real random responses, an experimental test administration was designed. Four different random response samples were produced using this experimental system.

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