Geodesic
Noncommutative enumeration in graded posets
Journal of Algebraic Combinatorics, Tome 12 (2000) no. 1, pp. 7-24.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: We define a noncommutative algebra of flag-enumeration functionals on graded posets and show it to be isomorphic to the free associative algebra on countably many generators. Restricted to Eulerian posets, this ring has a particularly appealing presentation with kernel generated by Euler relations. A consequence is that even on Eulerian posets, the algebra is free, with generators corresponding to odd jumps in flags. In this context, the coefficients of the cd-index provide a graded basis.
Keywords: graded poset, Eulerian poset, flag $f$-vector, flag $h$-vector, odd jumps, cd-index, coalgebra, Fibonacci 
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Billera, Louis J.; Liu, Niandong. Noncommutative enumeration in graded posets. Journal of Algebraic Combinatorics, Tome 12 (2000) no. 1, pp. 7-24. http://geodesic.mathdoc.fr/item/JAC_2000__12_1_a6/