Related papers: Landau's Theorem Revisited Again
The paper presents a hierarchical Bayesian model for simultaneous inference of tournament graphs and informant error. From multiple informant reports or measurement instrument outputs, the model estimates the structure of a criterion (i.e.,…
In this paper; we prove that all sequences can be broken up in cycles. Each cycle follows the same pattern: 1) Upward trajectory. Odd and even numbers alternate until the cycle reaches an upper bound 2) Downward trajectory. Two or more…
In J. Schwenk.(2018) ['What is the Correct Way to Seed a Knockout Tournament?' Retrieved from The American Mathematical Monthly], Schwenk identified a surprising weakness in the standard method of seeding a single elimination (or knockout)…
The classical rearrangement inequality provides bounds for the sum of products of two sequences under permutations of terms and show that similarly ordered sequences provide the largest value whereas opposite ordered sequences provide the…
We only consider finite structures. With every totally ordered set $V$ and a subset $P$ of $\binom{V}{2}$, we associate the underlying tournament ${\rm Inv}(\underline{V}, P)$ obtained from the transitive tournament $\underline{V}:=(V,…
We provide an algorithm with constant running time that given a weighted tournament $T$, distinguishes with high probability of success between the cases that $T$ can be represented by a Bradley--Terry model, or cannot even be approximated…
We study time scheduling problems with allowed absences as a new kind of graph coloring problem. One may think of a sport tournament where each player (each team) is permitted a certain number $t$ of absences. We then examine how many…
Replicability requires that algorithmic conclusions remain consistent when rerun on independently drawn data. A central structural question is composition: given $k$ problems each admitting a $\rho$-replicable algorithm with sample…
The Collatz sequence for a given natural number $N$ is generated by repeatedly applying the map $N$ $\rightarrow$ $3N+1$ if $N$ is odd and $N$ $\rightarrow$ $N/2$ if $N$ is even. One elusive open problem in Mathematics is whether all such…
Let ${\mathfrak S}_n$ denote the symmetric group with $n$ letters, and $g(n)$ the maximal order of an element of ${\mathfrak S}_n$. If the standard factorization of $M$ into primes is $M=q_1^{\al_1}q_2^{\al_2}... q_k^{\al_k}$, we define…
We define a game semantics for second order classical arithmetic PA2 (with quantifiers over predicates on integers and full comprehension axiom). Our semantics is effective: moves are described by a finite amount of information and whenever…
We prove a lower bound on the probability of Shor's order-finding algorithm successfully recovering the order $r$ in a single run. The bound implies that by performing two limited searches in the classical post-processing part of the…
Competition between a complex system's constituents and a corresponding reward mechanism based on it have profound influence on the functioning, stability, and evolution of the system. But determining the dominance hierarchy or ranking…
In this work, using the well-known mean-value theorem (Lagrange's theorem) we obtain an inequality for n-th order differential equations with retarded argument. If the retarded argument vanishes then the inequality turns to an inequality…
We answer the question of when a new point can be added in a continuous way to configurations of $n$ distinct points in a closed ball of arbitrary dimension. We show that this is possible given an ordered configuration of $n$ points if and…
In this article, we consider some simple combinatorial game and a winning strategy in this game. This game is then used to prove several known results about non-repetitive sequences and approximations with denominators from a lacunary…
The main theorem of this paper establishes conditions under which the "chaos game" algorithm almost surely yields the attractor of an iterated function system. The theorem holds in a very general setting, even for non contractive iterated…
We show that if $D$ is a tournament of arbitrary size then $D$ has finite strong components after reversing a locally finite sequence of cycles. In turn, we prove that any tournament can be covered by two acyclic sets after reversing a…
Given a sequence of $n$ numbers and $k$ parallel First-in-First-Out (FIFO) queues, how close can one bring the sequence to sorted order? It is known that $k$ queues suffice to sort the sequence if the Longest Decreasing Subsequence (LDS) of…
Consider the following one-player game. Take a well-formed sequence of opening and closing brackets. As a move, the player can pair any opening bracket with any closing bracket to its right, erasing them. The goal is to re-pair (erase) the…