Related papers: Unique Tournaments and Radar Tracking
It is "well known" that in linear models: (1) testable constraints on the marginal distribution of observed variables distinguish certain cases in which an unobserved cause jointly influences several observed variables; (2) the technique of…
In two-player games on graphs, the players move a token through a graph to produce an infinite path, which determines the winner of the game. Such games are central in formal methods since they model the interaction between a…
The Renyi-Ulam game is played between two players, the Seeker and the Obscurer. The Obscurer thinks of a number between 1 and $n$. The Seeker wishes to identify that number. On each turn, the Seeker asks the Obscurer whether her number…
In this paper, we completely characterize the niche graphs of bipartite tournaments and find their interesting properties.
The draw of some knockout tournaments requires finding a perfect matching in a balanced bipartite graph. The problem becomes challenging with draw constraints: the two draw procedures used in sports are known to be non-uniformly distributed…
We say a string has a cadence if a certain character is repeated at regular intervals, possibly with intervening occurrences of that character. We call the cadence anchored if the first interval must be the same length as the others. We…
Consider a two-player game between players Builder and Painter. Painter begins the game by picking a coloring of the edges of $K_n$, which is hidden from Builder. In each round, Builder points to an edge and Painter reveals its color.…
The Binary Two-Up Sequence is the lexicographically earliest sequence of distinct nonnegative integers with the property that the binary expansion of the n-th term has no 1-bits in common with any of the previous floor(n/2) terms. We show…
In this paper we study a variant of string pattern matching which deals with tuples of strings known as \textit{multi-track strings}. Multi-track strings are a generalisation of strings (or \textit{single-track strings}) that have primarily…
Mathematics has been used in the exploration and enumeration of juggling patterns. In the case when we catch and throw one ball at a time the number of possible juggling patterns is well-known. When we are allowed to catch and throw any…
Aboulker, Aubian, Charbit, and Lopes (2023) defined the clique number of a tournament to be the minimum clique number of one of its backedge graphs. Here we show that if $T$ is a tournament of sufficiently large clique number, then $T$…
We study the effects of randomness on competitions based on an elementary random process in which there is a finite probability that a weaker team upsets a stronger team. We apply this model to sports leagues and sports tournaments, and…
Competitive tournaments appear in sports, politics, population ecology, and animal behavior. All of these fields have developed methods for rating competitors and ranking them accordingly. A tournament is intransitive if it is not…
The classical paradox of social choice theory asserts that there is no fair way to deterministically select a winner in an election among more than two candidates; the only definite collective preferences are between individual pairs of…
Constructing a suitable schedule for sports competitions is a crucial issue in sports scheduling. The round-robin tournament is a competition adopted in many professional sports. For most round-robin tournaments, it is considered…
If the list of binary numbers is read by upward-sloping diagonals, the resulting ``sloping binary numbers'' 0, 11, 110, 101, 100, 1111, 1010, ... (or 0, 3, 6, 5, 4, 15, 10, ...) have some surprising properties. We give formulae for the n-th…
A central objective in Ramsey theory is determining whether restricted families of discrete structures necessarily contain substantially larger homogeneous substructures, compared to the unrestricted structures. In the setting of…
We investigate binary voting systems with two types of voters and a hierarchy among the members in each type, so that members in one class have more influence or importance than members in the other class. The purpose of this paper is to…
The chase is a fundamental algorithm with ubiquitous uses in database theory. Given a database and a set of existential rules (aka tuple-generating dependencies), it iteratively extends the database to ensure that the rules are satisfied in…
A chain is an ordering of the integers 1 to n such that adjacent pairs have sums of a particular form, such as squares, cubes, triangular numbers, pentagonal numbers, or Fibonacci numbers. For example 4 1 2 3 5 form a Fibonacci chain while…