학술
기타
A Snail Race Problem
arXiv Math
조회 0
이 뉴스, 어떠셨어요?
한 번의 탭으로 반응을 남겨요 · 로그인 불필요
CC BY
이 매체는 공공·자유 라이선스로 본문을 직접 표시합니다.Abstract
Inspired by Problem 17 from the 2024 American Mathematics Competition (AMC) 10B, this work focuses on enumerating the distinct outcomes of a snail race with specified number of ties of a certain type.
We begin by developing a recurrence relation and subsequently derive a closed-form formula for the number of possible outcomes using the exponential generating function method.
Two special cases of the problem are considered in detail.
Our analysis also explores the connections between the solution to this problem and the ordered Bell numbers, Stirling numbers of the second kind, and partial Bell polynomials.
관련 뉴스
관련 뉴스 제보는 로그인 후 가능합니다.
'research' 카테고리 뉴스
arXiv의 다른 기사
CreativityNeuro: Steering Language Model Weights to Improve Divergent Thinking and Reduce Mode Collapse
arXiv CS.AI
Discrete Diffusion Language Models for Interactive Radiology Report Drafting
arXiv CS.AI
Beyond Next-Token Prediction: An RLVR Proof of Concept for Tool-Use Agents on Atlassian Workflows
arXiv CS.AI