Algebraic and Combinatorial Properties of t-spread Strongly Stable Ideals

In this thesis, we study t-spread strongly stable monomial ideals. It is provedthat for an ideal to be t-spread strongly stable, it is sufficient for the definitioncriterion to be satisfied only on its minimal monomial generating set. The generators,height, Cohen-Macaulayness, and minimal free resolution of some special classesof t-spread strongly stable monomial ideals, namely, t-spread Veronese ideals andt-spread principal Borel ideals and their Alexander dual are studied. We also studythe Rees algebras of t-spread principal Borel ideals, and it is shown that they havethe so-called ℓ-exchange property. Consequently, the Rees algebra of a t-spreadprincipal Borel ideal is Koszul.