Acta Mathematica Vietnamica
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The First Syzygy of Hibi Rings Associated with Planar Distributive Lattices
Priya Das , Himadri Mukherjeepp. 689-707
Abstract
In this article, we give explicit minimal generators of the first syzygy of the Hibi ring for a planar distributive lattice in terms of sublattices. We also give a characterization when it is linearly related and derive an exact formula for the first Betti number of a planar distributive lattice.