Related papers: A Probabilistic Proof of the Multinomial Theorem

The purpose of this note is to give an affirmative answer to a conjecture appearing in [Integral Transforms Spec. Funct. 26 (2015) 90-95].

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with…

An approach is shown that proves various theorems of plane geometry in an algorithmic manner. The approach affords transparent proofs of a generalization of the Theorem of Morley and other well known results by casting them in terms of…

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…

This paper presents an offering of some of the myriad connections between Combinatorics and Probability, directed in particular toward combinatorialists. The choice of material was dictated by the author's own interests, tastes and…

In this article we demonstrate how algorithmic probability theory is applied to situations that involve uncertainty. When people are unsure of their model of reality, then the outcome they observe will cause them to update their beliefs. We…

Nonmonotonic reasoning is a pattern of reasoning that allows an agent to make and retract (tentative) conclusions from inconclusive evidence. This paper gives a possible-worlds interpretation of the nonmonotonic reasoning problem based on…

We prove an explicit Chinese Remainder Theorem for one variable polynomials with complex coefficients, and derive some consequences.

We discuss a version of the fundamental theorem of calculus in several variables and some applications, of potential interest as a teaching material in undergraduate courses.

(l) I have enough evidence to render the sentence S probable. (la) So, relative to what I know, it is rational of me to believe S. (2) Now that I have more evidence, S may no longer be probable. (2a) So now, relative to what I know, it is…

In this paper, we provide a probabilistic interpretation of the Volkenborn integral; this allows us to extend results by T. Kim et al about sums of Euler numbers to sums of Bernoulli numbers. We also obtain a probabilistic representation of…

This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…

We prove a multiple recurrence result for arbitrary measure-preserving transformations along polynomials in two variables of the form $m+p_i(n)$, with rationally independent $p_i$'s with zero constant term. This is in contrast to the single…

The probabilistic predictions of quantum theory are conventionally obtained from a special probabilistic axiom. But that is unnecessary because all the practical consequences of such predictions follow from the remaining, non-probabilistic,…

Bayesian probability theory is used as a framework to develop a formalism for the scientific method based on principles of inductive reasoning. The formalism allows for precise definitions of the key concepts in theories of physics and also…

We present an information theoretic proof of the nonsignalling multiprover parallel repetition theorem, a recent extension of its two-prover variant that underlies many hardness of approximation results. The original proofs used de Finetti…

In this note, we provide bijective proofs of some identities involving the Bell number, as previously requested. Our arguments may be extended to yield a generalization in terms of complete Bell polynomials. We also provide a further…

We give a proof of Cox's Theorem on the product rule and sum rule for conditional plausibility without assuming continuity or differentiablity of plausibility. Instead, we extend the notion of plausibility to apply to unknowns giving them…

We formulate the Hauptvermutung of Causal Set Theory in two mathematically well-defined but different ways one of which turns out to be wrong and the other one turns out to be true. A further result is that the Hauptvermutung is true if we…