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The r-cubical Lattice and a Generalization of the cd-index

✍ Scribed by Richard Ehrenborg; Margaret Readdy

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
390 KB
Volume
17
Category
Article
ISSN
0195-6698

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✦ Synopsis

In this paper we generalize the cd -index of the cubical lattice to an r -cd -index , which we denote by Γ• ( r ) . The coef ficients of Γ• ( r ) enumerate augmented Andre Β΄ r -signed permutations , a generalization of Purtill's work relating the cd -index of the cubical lattice and signed Andre Β΄ permutations . As an application we use the r -cd -index to determine that the extremal configuration which maximizes the Mo Β¨ bius function of arbitrary rank selections , where all the r i 's are greater than one , is the odd alternating ranks , Ν• 1 , 3 , 5 , . . . Ν– .

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