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On the Number of Iterations in a Kruskal-Type Process
Abstract
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,…,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 σ(m,n) for T, valid for every initial configuration of the deck, and to show that this bound is attained by a specific configuration.
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BibTeX
@misc{corregidor2026number,
title = {{On the Number of Iterations in a Kruskal-Type Process}},
author = {Samuel G. Corregidor},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29015},
eprint = {2610.29015},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29015},
}
RIS
TY - UNPB
TI - On the Number of Iterations in a Kruskal-Type Process
AU - Samuel G. Corregidor
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29015
UR - https://arxiv.org/abs/2610.29015
AB - 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,…,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 σ(m,n) for T, valid for every initial configuration of the deck, and to show that this bound is attained by a specific configuration.
ER -