Cohen-Macaulay Type of Weighted Path Ideals

Author

Shuai Wei, Clemson UniversityFollow

Date of Award

12-2022

Document Type

Dissertation

Degree Name

Doctor of Philosophy (PhD)

Department

Mathematical Sciences

Committee Chair/Advisor

Keri Sather-Wagstaff

Committee Member

Michael Burr

Committee Member

Shuhong Gao

Committee Member

Matthew Macauley

Abstract

In this dissertation we give a combinatorial characterization of all the weighted $r$-path suspensions for which the $f$-weighted $r$-path ideal is Cohen-Macaulay. In particular, it is shown that the $f$-weighted $r$-path ideal of a weighted $r$-path suspension is Cohen-Macaulay if and only if it is unmixed. Type is an important invariant of a Cohen-Macaulay homogeneous ideal in a polynomial ring $R$ with coefficients in a field. We compute the type of $R/I$ when $I$ is any Cohen-Macaulay $f$-weighted $r$-path ideal of any weighted $r$-path suspension, for some chosen function $f$. In particular, this computes the type for all weighted trees $T_\omega$ such that the corresponding ideal is Cohen-Macaulay.

Comments

Please use the latest submission, thank you

Recommended Citation

Wei, Shuai, "Cohen-Macaulay Type of Weighted Path Ideals" (2022). All Dissertations. 3248.
https://open.clemson.edu/all_dissertations/3248