We present what we call a "motivated proof" of the Andrews-Bressoud partition identities for even moduli. A "motivated proof" of the Rogers-Ramanujan identities was given by G. E. Andrews and R. J. Ba...

In his paper, "On a Partition Function of Richard Stanley," George Andrews proves a certain partition identity analytically and asks for a combinatorial proof. This paper provides the requested combin...

We give a new proof of Fitzgerald's criterion for primitive polynomials over a finite field. Existing proofs essentially use the theory of linear recurrences over finite fields. Here, we give a much s...

This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the...

The purpose of this paper is to prove directly, by an elementary method, the Poisson probability law. This proof is offered as an alternative to the more usual derivation from binomial distribution in...

Commercial Bank of Dubai (CBD) quadrupled its client base in the last four years, necessitating a future-proof banking platform. Using Microsoft Azure, CBD upgraded its application infrastructure, imp...

This repository contains code for demonstrating Arnold's topological proof of the Abel-Ruffini theorem that there is no general solution in radicals to polynomial equations of degree five or higher. (...

In 1967, Atkin and O'Brien conjectured congruences for the partition function involving Hecke operators modulo powers of 13. In this paper, we provide a simple proof of this conjecture....

MLL proof equivalence is the problem of deciding whether two proofs in multiplicative linear logic are related by a series of inference permutations. It is also known as the word problem for star-auto...

We give a new simpler proof of a theorem of Jayne and Rogers....

The no-supervenience theorem limits the capacity of physicalist theories to provide a comprehensive account of human consciousness. The proof of the theorem is difficult to formalize because it relies...

Poorly informed crypto-journalist articles are constantly coming out, and this brings more Proof-of-Stake related questions and discussions rehashing the same topics and same misconceptions. So here a...

In a world increasingly concerned with safety and security, the demand for high-performance bullet proof glass has grown substantially. From banking institutions and government facilities to schools.....

Future-proof your SEO strategy with Relevance Engineering, a new framework for AI search. Learn how to optimize content for LLMs, build topical authority, and adapt to Google's AI Mode for increased b...

We give an intuitive combinatorial proof of Ky Fan's covering lemma based on the Borsuk-Ulam theorem. We then show how this approach can be generalized to Ky Fan's covering lemma for several linear or...

Codes and Audits Proof of Gate holding full reserves of Users' assets (⭐ 373)

We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring ...

We present the first formal correctness proof of Edmonds' blossom shrinking algorithm for maximum cardinality matching in general graphs. We focus on formalising the mathematical structures and proper...

In this paper we present a complete proof of a conjecture due to V. V. Prelov in 2010 about an information inequality for the binary entropy function....

The fact she is in the Glow house, which is all about kindness and uplifting others, yet she’s racist? Not only is this proof that she’s racist but it’s also propf Gianna doesn’t genuinely car...