| Summary: | Let <i>K</i> be a field and let <inline-formula> <math display="inline"> <semantics> <mrow> <mi>S</mi> <mo>=</mo> <mi>K</mi> <mo>[</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>,</mo> <mo>⋯</mo> <mo>,</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo>]</mo> </mrow> </semantics> </math> </inline-formula> be a polynomial ring over <i>K</i>. We analyze the extremal Betti numbers of special squarefree monomial ideals of <i>S</i> known as the <i>t</i>-spread strongly stable ideals, where <i>t</i> is an integer <inline-formula> <math display="inline"> <semantics> <mrow> <mo>≥</mo> <mn>1</mn> </mrow> </semantics> </math> </inline-formula>. A characterization of the extremal Betti numbers of such a class of ideals is given. Moreover, we determine the structure of the <i>t</i>-spread strongly stable ideals with the maximal number of extremal Betti numbers when <inline-formula> <math display="inline"> <semantics> <mrow> <mi>t</mi> <mo>=</mo> <mn>2</mn> </mrow> </semantics> </math> </inline-formula>.
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