The Charney-Davis conjecture for simple thin polyominoes. Issue 4 (3rd April 2023)

• Record Type: Journal Article
• Authors: Kummini, Manoj; Veer, Dharm
• Is Part Of: Communications in algebra. Volume 51:Issue 4(2023)
• Page Start: 1654
• Page End: 1662
• Publication Date: 2023-04-03
• Subjects: Charney-Davis conjecture -- polyominoes; Primary: 13D40; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2022.2140347
• Languages: English
• ISSNs: 0092-7872

Abstract

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.