Related papers: Rhymes in primes
About twenty years ago, Green wrote a survey article on the utility of looking at toy versions over finite fields of problems in additive combinatorics. This article was extremely influential, and the rapid development of additive…
In this work we present a corpus of poems by William Shakespeare and John Milton that have been enriched with readings from the public domain. We have aligned all the lines with their respective audio segments, at the line, word, syllable…
Laudation delivered at the International Congress of Mathematicians in Berlin following the award of the Fields Medal to Richard Borcherds.
Since the advent of high-resolution pitch tracking data (PITCHf/x), many in the sabermetrics community have attempted to quantify a Major League Baseball catcher's ability to "frame" a pitch (i.e. increase the chance that a pitch is called…
This paper presents the results of the 2025 Automatic Music Transcription (AMT) Challenge, an online competition to benchmark progress in multi-instrument transcription. Eight teams submitted valid solutions; two outperformed the baseline…
Rich words are characterized by containing the maximum possible number of distinct palindromes. Several characteristic properties of rich words have been studied; yet the analysis of repetitions in rich words still involves some interesting…
Some misleading statements in a recent paper in PRE are corrected.
In this paper, we show that there is a one-to-one correspondence between the set of compositions (resp. prime compositions) of $n$ and the set of circulant digraphs (resp. connected circulant digraphs) of order $n$. We also show that there…
In the proposed matrix primes, through which one can readily generate a sequence of primes. The paper also proposes a number of theorems proved by which an infinite number of prime numbers twins
{\bf In the fourth extended version of this article, we provide a comprehensive historical survey of 200 different proofs of famous Euclid's theorem on the infinitude of prime numbers (300 {\small B.C.}--2022)}. The author is trying to…
In this paper, we prove certain theorems about three consecutive primes.
In this paper we study a sequence involving the prime numbers by deriving two asymptotic formulas and finding new upper and lower bounds, which improve the currently known estimates.
In [2], while studying a relevant class of polyominoes that tile the plane by translation, i.e., double square polyominoes, the authors found that their boundary words, encoded by the Freeman chain coding on a four letters alphabet, have…
Comments about the paper by Elsholz, Fermat's last theorem implies Euclid's infinitude of primes, (2021), and simplification.
We prove a generalization of the author's work to show that any subset of the primes which is `well-distributed' in arithmetic progressions contains many primes which are close together. Moreover, our bounds hold with some uniformity in the…
Reinforcement learning competitions advance the field by providing appropriate scope and support to develop solutions toward a specific problem. To promote the development of more broadly applicable methods, organizers need to enforce the…
We give a short appreciation of Robin Milner's seminal contributions to the theory of concurrency.
This is a manuscript accepted for publication on Physical Review Fluids, Gallery of Fluid Motion special issue. The manuscript is associated with a poster winner of the 39th Annual Gallery of Fluid Motion Award, for work presented at the…
In this paper, we make some conjectures on prime numbers that are sharper than those found in the current literature. First we describe our studies on Legendre's Conjecture which is still unsolved. Next, we show that Brocard's Conjecture…
We establish the existence of infinitely many \emph{polynomial} progressions in the primes; more precisely, given any integer-valued polynomials $P_1, >..., P_k \in \Z[\m]$ in one unknown $\m$ with $P_1(0) = ... = P_k(0) = 0$ and any $\eps…