Related papers: Unique Tournaments and Radar Tracking
We give three different computations of the total number of runs of length $i$ in binary $n$-strings, and we discuss the connection of this problem with the compositions of $n$.
A two-dimensional string is simply a two-dimensional array. We continue the study of the combinatorial properties of repetitions in such strings over the binary alphabet, namely the number of distinct tandems, distinct quartics, and runs.…
Observers in different inertial frames can see a set of spacelike separated events as occurring in different orders. Various restrictions are studied on the possible orderings of events that can be observed. In 1+1-dimensional spacetime {(1…
The Traveling Tournament Problem (TTP) is a hard but interesting sports scheduling problem inspired by Major League Baseball, which is to design a double round-robin schedule such that each pair of teams plays one game in each other's home…
In this paper, a track selection problem for multi-target tracking in a multifunction radar network is studied using the concepts from game theory. The problem is formulated as a non-cooperative game, and specifically as an…
Every sport needs rules. Tournament design refers to the rules that determine how a tournament, a series of games between a number of competitors, is organized. This study aims to provide an overview of the tournament design literature from…
An infinite binary sequence is deemed to be random if it has all definable properties that hold almost surely for the usual probability measure on the set of infinite binary sequences. There are only countably many such properties, so it…
We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…
A diamond is a $4$-tournament which consists of a vertex dominating or dominated by a $3$-cycle. Assuming the existence of skew-conference matrices, we give a complete characterization of $n$-tournaments with the maximum number of diamonds…
We consider the problem of inferring an unknown ranking of $n$ items from a random tournament on $n$ vertices whose edge directions are correlated with the ranking. We establish, in terms of the strength of these correlations, the…
Two Beatty sequences are recorded by athletes running in opposite directions in a round stadium. This approach suggests a nice interpretation for well known partitioning criteria: such sequences (eventually) partition the integers…
We consider a general class of round-robin tournament models of equally strong players. In these models, each of the $n$ players competes against every other player exactly once. For each match between two players, the outcome is a value…
A knockout tournament is one of the most simple and popular forms of competition. Here, we are given a binary tournament tree where all leaves are labeled with seed position names. The players participating in the tournament are assigned to…
Let $T$ be a tournament with nondecreasing score sequence $R$ and $A$ be its tournament matrix. An upset of $T$ corresponds to an entry above the main diagonal of $A$. Given a feasible score sequence $R$, Fulkerson~(1965) gave a simple…
Given a Dirichlet eigenfunction of a 2D quantum billiard, the boundary domain count is the number of intersections of the nodal lines with the boundary. We study the integer sequence defined by these numbers, sorted according to the…
We consider the manipulability of tournament rules for round-robin tournaments of $n$ competitors. Specifically, $n$ competitors are competing for a prize, and a tournament rule $r$ maps the result of all $\binom{n}{2}$ pairwise matches…
Ladder tournaments are widely used to rank individuals in real-world organizations and games. Their mathematical properties however are still poorly understood. We formalize the ranking rule generated by a ladder tournament, and we show…
The traveling tournament problem (TTP) is to minimize the total traveling distance of all teams in a double round-robin tournament. In this paper, we focus on TTP-2, in which each team plays at most two consecutive home games and at most…
A tournament is called locally transitive if the outneighbourhood and the inneighbourhood of every vertex are transitive. Equivalently, a tournament is locally transitive if it avoids the tournaments $W_4$ and $L_4$, which are the only…
Ranking the participants of a tournament has applications in voting, paired comparisons analysis, sports and other domains. In this paper we introduce bipartite tournaments, which model situations in which two different kinds of entity…