The Eulerian polynomial \( \mathrm {AExc}_n(t)\) enumerating excedances in the symmetric group \(\mathfrak {S}_n\) is known to be gamma positive for all n. When enumeration is done over the type B and type D Coxeter groups, the type B and type D Eulerian polynomials are also gamma positive for all n. We consider \( \mathrm {AExc}_n^+(t)\) and \( \mathrm {AExc}_n^-(t)\), the polynomials which enumerate excedance in the alternating group \(\mathcal {A}_n\) and in \(\mathfrak {S}_n - \mathcal {A}_n\), respectively. We show that \( \mathrm {AExc}_n^+(t)\) is gamma positive iff \(n \ge 5\) is odd. When \(n \ge 4\) is even, \( \mathrm {AExc}_n^+(t)\) is not even palindromic, but we show that it is the sum of two gamma positive summands. An identical statement is true about \( \mathrm {AExc}_n^-(t)\). We extend similar results to the excedance based Eulerian polynomial when enumeration is done over the positive elements in both type B and type D Coxeter groups. Gamma positivity results are known when excedance is enumerated over derangements in \(\mathfrak {S}_n\). We extend some of these to the case when enumeration is done over even and odd derangements in \(\mathfrak {S}_n\).

欧拉多项式\（\ mathrm {AExc} _n（t）\）枚举对称组\（\ mathfrak {S} _n \）中的阶跃对所有n都是伽马正数。当对类型B和类型D的Coxeter组进行枚举时，对于所有n，类型B和类型D的欧拉多项式也是伽玛正的。我们考虑\（\ mathrm {AExc} _n ^ +（t）\）和\（\ mathrm {AExc} _n ^-（t）\），它们是交替组\（\ mathcal {A} _n \）和\（\ mathfrak {S} _n-\ mathcal {A} _n \）中。我们证明\（\ mathrm {AExc} _n ^ +（t）\）是伽玛正的iff \（n \ ge 5 \）很奇怪 当\（n \ ge 4 \）是偶数时，\（\ mathrm {AExc} _n ^ +（t）\）甚至不是回文的，但是我们证明它是两个伽马正加和的和。关于\（\ mathrm {AExc} _n ^-（t）\），同样的说法是正确的。当对B型和D型Coxeter组中的正元素进行枚举时，我们将相似的结果扩展到基于超越的欧拉多项式。当对\（\ mathfrak {S} _n \）中的异常点进行计数时，会得出伽马阳性结果。我们将其中一些扩展到对\（\ mathfrak {S} _n \）中的偶数和奇数排列进行枚举的情况。