论文标题
B型的1/K-Eulerian多项式
The 1/k-Eulerian polynomials of type B
论文作者
论文摘要
在本文中，我们给出了1/k-eulerian多项式的B型类似物。研究了这种多项式的特性，包括组合解释，复发关系和伽马积极性。特别是，我们表明，当$ k> 0 $时，B型的1/k-eulerian多项式是伽马阳性的。此外，我们获得了B型扰动的相应结果。我们表明，当$ k \ geq 1/2 $时，B 1/kderangement多项式$ d_n^b（x; k）$是bi-gamma阳性。特别是，我们在经典的扰动多项式方面得到了$ d_n^b（x; 1/2）$的对称分解。
In this paper, we give a type B analogue of the 1/k-Eulerian polynomials. Properties of this kind of polynomials, including combinatorial interpretations, recurrence relations and gamma-positivity are studied. In particular, we show that the 1/k-Eulerian polynomials of type B are gamma-positive when $k>0$. Moreover, we obtain the corresponding results for derangements of type B. We show that a type B 1/k-derangement polynomials $d_n^B(x;k)$ are bi-gamma-positive when $k\geq 1/2$. In particular, we get a symmetric decomposition of $d_n^B(x;1/2)$ in terms of the classical derangement polynomials.
