(untitled) (Journal of Mathematical Study, 2024)
In this paper, we study some basic analytic properties of a sequence of functions {S^μ,σ_n} that is directly derived in an adaptive algorithm originating from the classical score-based secretary problem. More specifically, we show that: 1. the uniqueness of maximum points of the function sequence {S^μ,σ_n}; 2. the maximum point sequence of {S^μ,σ_n} monotone increases to infinity as n tends to infinity. All of the proofs are elementary but nontrivial.