Distributions of successions of arbitrary multisets

TL;DR

This paper develops a matrix-based method to derive explicit formulas for the distributions, means, and variances of successions in random permutations of arbitrary multisets, advancing combinatorial probability analysis.

Contribution

It introduces a matrix formulation approach to obtain recurrence and explicit formulas for successions in permutations of multisets, including mean and variance calculations.

Findings

Derived recurrence formulas for successions in multisets

Obtained explicit formulas for generating functions

Calculated mean and variance of successions

Abstract

By using the matrix formulation of the two-step approach to distributions of patterns in random sequences, recurrence and explicit formulas for the generating functions of successions in random permutations of arbitrary multisets are derived. Explicit formulas for the mean and variance are also obtained.