@article{oai:soar-ir.repo.nii.ac.jp:00019878, author = {Maeno, Toshiaki and Numata, Yasuhide}, issue = {4}, journal = {JOURNAL OF COMMUTATIVE ALGEBRA}, month = {}, note = {We prove the Lefschetz property for a certain class of finite-dimensional Gorenstein algebras associated to matroids. Our result implies the Sperner property of the vector space lattice. More generally, it is shown that the modular geometric lattice has the Sperner property. We also discuss the Grobner fan of the de fining ideal of our Gorenstein algebra., Article, JOURNAL OF COMMUTATIVE ALGEBRA. 8(4):549-570 (2016)}, pages = {549--570}, title = {Sperner property and finite-dimensional Gorenstein algebras associated to matroids}, volume = {8}, year = {2016} }