We present a MATLAB package, which is the first of its kind, for Higher Order Markov Chains (HOMC). It can be used to easily compute all important quantities in our recent works relevant to higher order Markov chains, such as the $k$-step transition tensor, limiting probability distribution, ever-reaching probability tensor, and mean first passage time tensor. It can also be used to check whether a higher order chain is ergodic or regular, to construct the transition matrix of the associated reduced first order chain, and to determine whether a state is recurrent or transient. A key function in the package is an implementation of the tensor ``box'' product which has a probabilistic interpretation and is different from other tensor products in the literature. This HOMC package is useful to researchers and practitioners alike for tasks such as numerical experimentation and algorithm prototyping involving higher order Markov chains.

翻译：本文介绍了一款MATLAB软件包，该软件包是首个用于高阶马尔可夫链（HOMC）的工具。它可以便捷地计算我们近期工作中与高阶马尔可夫链相关的所有重要量，例如$k$步转移张量、极限概率分布、可达概率张量以及平均首达时间张量。该软件包还可用于检验高阶链是否具有遍历性或正则性，构建对应的降阶一阶链的转移矩阵，并判断状态是常返态或瞬态。软件包中的一个关键函数实现了张量的“盒”积运算，该运算具有概率解释，且与文献中的其他张量积不同。此HOMC软件包对研究者和实践者均具有实用价值，可用于涉及高阶马尔可夫链的数值实验和算法原型开发等任务。