Tian-Xiao He

collaborators

2 papers

math.CO2023

The $m$ th-order Eulerian Numbers

Tian-Xiao He

We define the $m$ th-order Eulerian numbers with a combinatorial interpretation. The recurrence relation of the $m$ th-order Eulerian numbers, the row generating function and the row…

math.CO2023

Divisibility of the Sums of the Power of Consecutive Integers

Tian-Xiao He, Peter J. -S. Shiue

We study the divisibility of the sums of the odd power of consecutive integers, $S (m, k) = 1^{mk} + 2^{mk} + \dots + k^{mk}$ and $1^{k} + 2^{k} + \dots + n^{k}$ for odd integers $m$ and $k$ , by using…

The mth-order Eulerian Numbers

Divisibility of the Sums of the Power of Consecutive Integers

The $m$ th-order Eulerian Numbers