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Pascal type properties of Betti numbers

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  • Tilak de Alwis

Abstract

In this paper, we will describe the Pascal Type properties of Betti numbers of ideals associated to n -gons. These are quite similar to the properties enjoyed by the Pascal's Triangle, concerning the binomial coefficients. By definition, the Betti numbers β t ( n ) of an ideal I associated to an n -gon are the ranks of the modules in a free minimal resolution of the R -module R / I , where R is the polynomial ring k [ x 1 , x 2 , … , x n ] . Here k is any field and x 1 , x 2 , … , x n are indeterminates. We will prove those properties using a specific formula for the Betti numbers.

Suggested Citation

  • Tilak de Alwis, 1994. "Pascal type properties of Betti numbers," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 17, pages 1-8, January.
    • Handle: RePEc:hin:jijmms:210823
    DOI: 10.1155/S0161171294000797
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