Dear All,
We are pleased to invite you to the IEOR Seminar by Hikaru Manabe and Takahiro Yamashita on 28 October 2025.
Date and Time: 28 October 2025 (Tuesday), 11:35 a.m.– 12:35 p.m.
Venue: IEOR Seminar Room
Title: The Dragon-fly Moth Game and polygonal numbers, and when Maximum Restricted Nim meets Josephus Problem
Speakers: Hikaru Manabe (University of Tsukuba) and Takahiro Yamashita (Hiroshima University)
Abstract: (Hikaru) We will talk about the relationship between Max-restricted Nim and the Josephus Problem. Max-restricted Nim, introduced by Levin, is a variant of Nim where the number of stones one can take from a pile of size m is limited by a rule function, f(m). The Josephus Problem is a well-known mathematical puzzle dating back to antiquity. In this problem, people are arranged in a circle, and proceeding in one direction, every k-th person is removed to determine the final survivor. I will explain an interesting property of this game's Grundy number sequence and provide an intuition for how it elegantly relates to the Josephus Problem. (Takahiro) Dragonfly and Moss is two-player two piles Nim game. A player takes at lest two stones from one pile and return at least one stone to the other pile so that the total number of stones decreases, or they take i>0 stones from one pile together with j >0 tokens from the other pile so that |i-j|<=c, where c is a given game parameter. Surprisingly, the P-positions correspond to polygonal numbers. For example, if c=0, the set of P-positions describes {(0,0), (0,1), (1,3), (3,6), (6,10), …}, and the Triangle Number appears. We will explain why this happens.
Bios:
Hikaru Manabe is a first-year undergraduate student at the University of Tsukuba, Japan. His research focuses on Combinatorial Game Theory, and he is currently a visiting researcher in the Department of Industrial Engineering and Operations Research at the Indian Institute of Technology Bombay. He has received several awards from organizations such as the IEEE and the Information Processing Society of Japan (IPSJ). Additionally, he has experience as a session chair at an international conference and he is organizing a conference in this field. In the last three years, he has published 11 papers in Scopus-indexed journals and delivered 40 presentations at domestic and international conferences.
Takahiro Yamashita is an 3rd Grade Ph.D Student at the Department of Mathematics Hiroshima University, Japan. He is a student in Combinatorial Game Theory. His main topic revolves around Impartial Subtraction Games. He is the one of the organizer of the International Conference on Combinatorial Game Theory in Japan that will be held on March, 2026.
Host: Prof. Urban Larsson