A combinatorial proof of q-log-concavity of q-Eulerian numbers

被引：0
|
作者：
Liu, Xinmiao [1 ]
Hou, Jiangxia [1 ]
Liu, Fengxia [1 ]
机构：
[1] Xinjiang Univ, Coll Math & Syst Sci, Urumqi 830046, Xinjiang, Peoples R China
来源：
RAMANUJAN JOURNAL | 2024年 / 64卷 / 03期
基金：
中国国家自然科学基金;
关键词：
q-Log-concavity; q-Eulerian number; Lattice path; Injective map;
D O I：
10.1007/s11139-024-00841-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Carlitz established a q-analog of the Eulerian numbers A(n,k)(q) and defined the relationship A(n,k)(q) = q (n-k)(n-k+1)/ 2 A(n,k)(& lowast;)(q). In this paper, by using the combinatorial interpretation of A(n,k)(& lowast;)(q) and constructing injective maps, we prove that A(n,k)(& lowast;)(q) and A(n,k)(& lowast;)(q) are q-log-concave, that is, all the coefficients of the polynomials A(n,k)(& lowast;)(q))(2 )- A(n,k-1)(& lowast;)(q) A(n,k+1)*(q) and (A(n,k)(q))(2 )- A(n,k-1)(q) A(n,k+1)(q) are nonnegative for 1<k<n.
引用
收藏
页码：709 / 719
页数：11
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