Product (mathematics)

About: Product (mathematics) is a research topic. Over the lifetime, 44382 publications have been published within this topic receiving 377809 citations.

Method of probabilistically modeling variables

Abstract: A method 10 for analyzing the attribute of a product by probabilistically modeling certain variables associated with the product.

Dynamic Assortment Optimization for Reusable Products with Random Usage Durations

Abstract: We consider dynamic assortment problems with reusable products, in which each arriving customer chooses a product within an offered assortment, uses the product for a random duration of time, and r...

Noncommutative symmetric functions III : D eformations of C auchy and convolution algebras

Abstract: This paper discusses various deformations of free associative algebras and of their convolution algebras Our main examples are deformations of noncommutative symmetric functions related to families of idempotents in descent algebras, and a simple q -analogue of the shuffle product, which has unexpected connections with quantum groups, hyperplane arrangements, and certain questions in mathematical physics (the quon algebra, generalized Brownian motion)

A probabilistic technique for finding almost-periods of convolutions

Abstract: We introduce a new probabilistic technique for finding 'almost-periods' of convolutions of subsets of groups. This gives results similar to the Bogolyubov-type estimates established by Fourier analysis on abelian groups but without the need for a nice Fourier transform to exist. We also present applications, some of which are new even in the abelian setting. These include a probabilistic proof of Roth's theorem on three-term arithmetic progressions and a proof of a variant of the Bourgain-Green theorem on the existence of long arithmetic progressions in sumsets A+B that works with sparser subsets of {1, ..., N} than previously possible. In the non-abelian setting we exhibit analogues of the Bogolyubov-Freiman-Halberstam-Ruzsa-type results of additive combinatorics, showing that product sets A B C and A^2 A^{-2} are rather structured, in the sense that they contain very large iterated product sets. This is particularly so when the sets in question satisfy small-doubling conditions or high multiplicative energy conditions. We also present results on structures in product sets A B. Our results are 'local' in nature, meaning that it is not necessary for the sets under consideration to be dense in the ambient group. In particular, our results apply to finite subsets of infinite groups provided they 'interact nicely' with some other set.

Tropical intersection theory from toric varieties

Abstract: We apply ideas from intersection theory on toric varieties to tropical intersection theory. We introduce mixed Minkowski weights on toric varieties which interpolate between equivariant and ordinary Chow cohomology classes on compact toric varieties. These objects fit into the framework of tropical intersection theory developed by Allermann and Rau. Standard facts about intersection theory on toric varieties are applied to show that the definitions of tropical intersection product on tropical cycles in $${\mathbb{R}^n}$$ given by Allermann–Rau and Mikhalkin are equivalent. We introduce an induced tropical intersection theory on subvarieties on a toric variety. This gives a conceptual proof that the intersection of tropical ψ-classes on $${\overline{\mathcal{M}}_{0,n}}$$ used by Kerber and Markwig computes classical intersection numbers.