Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Mathematical Sciences

Committee Chair/Advisor

Keri Sather-Wagstaff

Committee Member

Michael Burr

Committee Member

Shuhong Gao

Committee Member

Matthew Macauley


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.


Please use the latest submission, thank you

Included in

Algebra Commons



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