Journal of Mathematical Chemistry

, Volume 57, Issue 2, pp 655–689 | Cite as

Computational multinomial combinatorics for colorings of 5D-hypercubes for all irreducible representations and applications

  • Krishnan BalasubramanianEmail author
Original Paper


We have developed computational multinomial techniques for colorings of 5D-hypercubes for all irreducible representations of the five-dimensional hyperoctahedral group up to 10 different color types. We have used the computed character tables of the 5D-hyperoctahedral group of order 3840 with 36 irreducible representations to obtain multinomial generating functions for coloring combinatorics for all irreducible representations. Explicit tables are provided for coloring tesseracts of 5D-hypercubes up to 10 colors for all 36 irreducible representations, 32 vertices and 80 faces of the 5D-hypercube. A number of chemical applications to non-rigid molecules and weakly-bound clusters such as (H2O)5, (Cl2O)5, (OF2)5, and non-rigid pseudo-rotating pentacoordinated complexes such as Co(H2O) 5 3+ as well as to genetic regulatory networks are outlined.


5D-hypercube Combinatorial enumerations Character table Coloring 5D-hypercube Nuclear spin statistics Generalized Pólya theory 


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Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Molecular SciencesArizona State UniversityTempeUSA

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