TY - JOUR
T1 - The lefschetz property for barycentric subdivisions of shellable complexes
AU - Kubitzke, Martina
AU - Nevo, Eran
PY - 2009/11
Y1 - 2009/11
N2 - We show that an 'almost strong Lefschetz' property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a Cohen-Macaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M-sequence. In particular, the (combinatorial) g-conjecture is verified for barycentric subdivisions of homology spheres. In addition, using the above algebraic result, we derive new inequalities on a refinement of the Eulerian statistics on permutations, where permutations are grouped by the number of descents and the image of 1.
AB - We show that an 'almost strong Lefschetz' property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a Cohen-Macaulay complex, the h-vector is unimodal, peaks in its middle degree (one of them if the dimension of the complex is even), and that its g-vector is an M-sequence. In particular, the (combinatorial) g-conjecture is verified for barycentric subdivisions of homology spheres. In addition, using the above algebraic result, we derive new inequalities on a refinement of the Eulerian statistics on permutations, where permutations are grouped by the number of descents and the image of 1.
KW - Barycentric subdivision
KW - Lefschetz
KW - Shellable
KW - Stanley-Reisner ring
UR - http://www.scopus.com/inward/record.url?scp=77950638009&partnerID=8YFLogxK
U2 - 10.1090/S0002-9947-09-04794-1
DO - 10.1090/S0002-9947-09-04794-1
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AN - SCOPUS:77950638009
SN - 0002-9947
VL - 361
SP - 6151
EP - 6163
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
IS - 11
ER -