The Charney-Davis conjecture for simple thin polyominoes. Issue 4 (3rd April 2023) - Kummini, Manoj; Veer, Dharm
Abstract: Let P be a simple thin polyomino and k a field. Let R be the toric k -algebra associated to P . Write the Hilbert series of R as h R ( t ) / ( 1 − t ) dim ( R ) . We show that M0001 ( − 1 ) ⌊ deg h R ( t ) 2 ⌋ h R ( − 1 ) ≥ 0 if R is Gorenstein. This shows that the Gorenstein rings associated to simple thin polyominoes satisfy the Charney-Davis conjecture.