cluster character
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2011 ◽  
Vol 54 (1) ◽  
pp. 27-60 ◽  
Author(s):  
IBRAHIM ASSEM ◽  
GRÉGOIRE DUPONT ◽  
RALF SCHIFFLER ◽  
DAVID SMITH

AbstractTo any walk in a quiver, we associate a Laurent polynomial. When the walk is the string of a string module over a 2-Calabi–Yau tilted algebra, we prove that this Laurent polynomial coincides with the corresponding cluster character of the string module up to an explicit normalising monomial factor.


2005 ◽  
Vol 70 (4) ◽  
pp. 410-429 ◽  
Author(s):  
Jonathan Bould ◽  
Mark Bown ◽  
John D. Kennedy

[(η6-C6Me6)RuOB9H13], obtained in trace yield from the reaction between [{RuCl2(η6-C6Me6)}2] and the [arachno-B6H11]- anion, has been shown by DFT calculations of structure and of boron-atom nuclear shielding to be of an arachno eleven-vertex cluster geometry that is derived by the removal of adjacent six-connected and five-connected vertices from a closed thirteen-vertex deltahedral 1:6:5:1 stack. The results lead to further considerations in oxaborane chemistry, which are explored and consolidated by calculation. Additional products from the reaction include [4-(η6-C6Me6)-n-arachno-4-RuB8H14], also substantiated by DFT calculations, and several four-, five-, six-, nine- and ten-vertex ruthenaboranes that are either known compounds or simple variants of known compounds.


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