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math.AC2021★ 3 cited
On the Purity of Resolutions of Stanley-Reisner Rings Associated to Reed-Muller Codes
Sudhir R. Ghorpade, Rati Ludhani
Following Johnsen and Verdure (2013), we can associate to any linear code an abstract simplicial complex and in turn, a Stanley-Reisner ring . The ring is a standard…
math.AC2018
A Note on Nullstellensatz over Finite Fields
Sudhir R. Ghorpade
We give an expository account of Nullstellensatz-like results when the base field is finite. In particular, we discuss the vanishing ideal of the affine space and of the projective…
math.AC2001
The Hilbert Series of Pfaffian Rings
Sudhir R. Ghorpade, Christian Krattenthaler
We give three determinantal expressions for the Hilbert series as well as the Hilbert function of a Pfaffian ring, and a closed form product formula for its multiplicity. An append…