On the Number of Iterations in a Kruskal-Type Process

Motivated by the Kruskal counting procedure, this paper investigates a combinatorial elimination process defined on a deck consisting of $m$ copies of each value $1,2,\dots ,n$. Starting from an arbitrary arrangement of the $mn$ cards, the process repeatedly removes a number of consecutive cards equal to the value of the first remaining card. This generates a sequence of elimination steps whose length determines $T$, representing the total number of iterations required to exhaust the deck. The main objective of this paper is to analyze an upper bound $\sigma (m,n)$ for $T$, valid for every initial configuration of the deck, and to show that this bound is attained by a specific configuration.