Geodesic
Face numbers and nongeneric initial ideals
The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2
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Certain necessary conditions on the face numbers and Betti numbers of simplicial complexes endowed with a proper action of a prime order cyclic group are established. A notion of colored algebraic shifting is defined and its properties are studied. As an application a new simple proof of the characterization of the flag face numbers of balanced Cohen-Macaulay complexes originally due to Stanley (necessity) and Björner, Frankl, and Stanley (sufficiency) is given. The necessity portion of their result is generalized to certain conditions on the face numbers and Betti numbers of balanced Buchsbaum complexes.
DOI : 10.37236/1882
Classification : 52B05, 13F55
Mots-clés : Betti numbers, Cohen-Macaulay complex, simplicial complex, face numbers, initial ideal, Stanley-Reisner ideal, algebraic shifting 
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     author = {Eric Babson and Isabella Novik},
     title = {Face numbers and nongeneric initial ideals},
     journal = {The electronic journal of combinatorics},
     year = {2004},
     volume = {11},
     number = {2},
     doi = {10.37236/1882},
     zbl = {1085.52004},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1882/}
}
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Eric Babson; Isabella Novik. Face numbers and nongeneric initial ideals. The electronic journal of combinatorics, The Stanley Festschrift volume, Tome 11 (2004) no. 2. doi: 10.37236/1882

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