Unique Tournaments and Radar Tracking

TL;DR

This paper reveals a surprising connection between counting unique tournaments among n people and non-tracking binary strings in radar observations, establishing a bijection that links these two combinatorial structures.

Contribution

It introduces a novel bijection between unique tournaments and non-tracking binary strings, connecting two previously unrelated combinatorial sequences.

Findings

The sequence of unique tournaments matches the sequence of non-tracking binary strings.

A bijection between unique tournaments and non-tracking strings is constructed.

This connection provides new insights into combinatorial enumeration and radar tracking models.

Abstract

The sequence counting the number of unique tournaments with n people is the same as the sequence counting non-tracking binary strings corresponding to n-2 radar observations with the tracking rule "3 out of 5 with loss 2." This fact allows us to build a bijection between unique tournaments and non-tracking binary strings.