The USCI approach and elementary superposition for combinatorial enumeration

1992 ◽  
Vol 82 (6) ◽  
pp. 473-498 ◽  
Author(s):  
Shinsaku Fujita
Keyword(s):  
Combinatorial Enumeration ◽  
Usci Approach

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).

An Introductory Set of Activities Designed to Facilitate Successful Combinatorial Enumeration for Undergraduate Students

PRIMUS ◽  
2016 ◽  
Vol 26 (10) ◽  
pp. 889-904
Author(s):  
Elise Lockwood ◽  
Craig A. Swinyard
Keyword(s):  
Undergraduate Students ◽  
Combinatorial Enumeration

Subduction of Q-conjugacy representations and characteristic monomials for combinatorial enumeration

1998 ◽  
Vol 99 (4) ◽  
pp. 224-230 ◽  
Author(s):  
Shinsaku Fujita
Keyword(s):  
Combinatorial Enumeration

Combinatorial enumeration in chemistry

2007 ◽  
pp. 126-170 ◽  
Author(s):  
D. Babic ◽  
D. J. Klein ◽  
J. Von Knop ◽  
N. Trinajstic
Keyword(s):  
Combinatorial Enumeration

scholarly journals Combinatorial Enumeration of Graphs

2020 ◽  
Author(s):  
Carlos Rodríguez Lucatero
Keyword(s):  
Combinatorial Enumeration

scholarly journals Combinatorial enumeration of cyclic covers of P1

2018 ◽  
Vol 42 (4) ◽  
pp. 2018-2034
Author(s):  
Alberto BESANA ◽  
Cristina MARTINEZ
Keyword(s):  
Combinatorial Enumeration ◽  
Cyclic Covers
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