The estimation of the zeros of the Bell and r-Bell polynomials

Real zeros and partitions without singleton blocks

“…for any fixed k. From this it will follow at once that the asymptotics (17) holds. What is more, relying on (18) and following the proof presented in [17] and in its references one can prove that the maximizing index is close…”

“…What is more, relying on (18) and following the proof presented in [17] and in its references one can prove that the maximizing index is close to n − 1…”

Asymptotics of the modes of the ordered Stirling numbers

“…It is conjectured by Wegner that S(n, K * n ) > S(n, K * n + 1), that is, the maximum is unique for n > 2 (see also [5,7]). There are good estimations for the mode K * n , it asymptotically equals to n/ log(n) (see [8] for a short proof).…”