Related papers: A Million-dollar Proof
We present a new alternating convolution formula for the super Catalan numbers which arises as a generalization of two known binomial identities. We prove a generalization of this formula by using auxiliary sums, recurrence relations, and…
We present what we call a "motivated proof" of the Bressoud-G\"ollnitz-Gordon partition identities. Similar "motivated proofs" have been given by Andrews and Baxter for the Rogers-Ramanujan identities and by Lepowsky and Zhu for Gordon's…
We prove some extensions of Andrews inequality.
Anonymity of both natural and legal persons in court rulings is a critical aspect of privacy protection in the European Union and Switzerland. With the advent of LLMs, concerns about large-scale re-identification of anonymized persons are…
Authorship identification has proven unsettlingly effective in inferring the identity of the author of an unsigned document, even when sensitive personal information has been carefully omitted. In the digital era, individuals leave a…
We give a new expression of the multiple harmonic sum, which serves as a refinement of the iterated integral expression of the multiple zeta value, and prove it using the so-called connected sum method. Based on this fact, by taking two…
The new paper will be submitted.
The identity by Chaundy and Bullard expresses $1$ as a sum of two truncated binomial series in one variable where the truncations depend on two different non-negative integers. We present basic and elliptic extensions of the…
In this paper we give a computer proof of a new polynomial identity, which extends a recent result of Alladi and the first author. In addition, we provide computer proofs for new finite analogs of Jacobi and Euler formulas. All computer…
We prove a family of new identities fulfilled by multinomial coefficients, which were conjectured by Dykema and Haagerup. Our method bases on a study of the, so-called, triangular operator T by the means of the free probability theory.
Automatic theorem proving with deep learning methods has attracted attentions recently. In this paper, we construct an automatic proof system for trigonometric identities. We define the normalized form of trigonometric identities, design a…
In this note, we present a curious $q$-series identity with applications to certain partitions with bounded part differences.
The 1-identification problem is a fundamental pure-exploration problem in multi-armed bandits. An agent aims to determine whether there exists an arm whose mean reward exceeds a known threshold $\mu_0$, or to output \textsf{None} otherwise.…
A formal computation proving a new operator identity from known ones is, in principle, restricted by domains and codomains of linear operators involved, since not any two operators can be added or composed. Algebraically, identities can be…
In this paper, we first give a simple combinatorial proof of Tepper's identity. Then, as a by product of this interesting identity we present another proof of the well-known Wilson's identity in number theory. Finally, we obtain a…
In this paper we prove a new degenerated version of Fay's trisecant identity. The new identity is applied to construct new algebro-geometric solutions of the multi-component nonlinear Schr\"odinger equation. This approach also provides an…
Using a probabilistic approach, we derive some interesting combinatorial identities involving gamma and beta functions. These results generalize certain well-known combinatorial identities involving binomial coefficients and special…
The author proves variants of Buchstab's identity on sieve functions, refining the previous work on new iteration rules of Brady. The main tool used in the proof is a special form of combinatorial identities related to the binomial…
Person re-identification consists in recognizing an individual that has already been observed over a network of cameras. It is a novel and challenging research topic in computer vision, for which no reference framework exists yet. Despite…
We present a novel blockchain based service for proving the provenance of online digital identity, exposed as an assistive tool to help non-expert users make better decisions about whom to trust online. Our service harnesses the digital…