Moderate Growth Time Series for Dynamic Combinatorics Modelisation

TL;DR

This paper introduces a new family of time series with growth constraints, useful for modeling local rule-based computations in business and micro-economics, and establishes their statistical properties and connections to ballot-like structures.

Contribution

It defines a novel class of growth-constrained time series and links their statistics to ballot-like combinatorial structures.

Findings

Established a one-to-one correspondence with ballot-like structures.

Derived explicit double statistics for the series.

Provided a potential modeling framework for economic computations.

Abstract

Here, we present a family of time series with a simple growth constraint. This family can be the basis of a model to apply to emerging computation in business and micro-economy where global functions can be expressed from local rules. We explicit a double statistics on these series which allows to establish a one-to-one correspondence between three other ballot-like strunctures.