This "homc" holder contains the functions of the HOMC package, as described in "HOMC: A MATLAB package for higher order Markov chains", available at: 
https://doi.org/10.48550/arXiv.2510.02664

The additional "ext" folder contains the following three new functions:
bprode
bpowe
eyete
These functions are extensions of bprod, bpow, and eyet of the original HOMC package. They are useful in partitioned box products and powers of transition tensors. For m-th order n x ... x n tensors, they work exactly as bprod, bpow, and eyet. They will replace bprod, bpow, and eyet in the near future.

The function C=eyete(s) constructs the m-th order u x u x n x ... x n identity tensor 
[delta_{i_1i_2 ... i_m}],
where s must be the m-vector [u u n ... n]. By definition,
delta_{i_1i_2 ... i_m}=delta_{i_1i_2}.

The function C=bprode(A,B) computes the box product of an m-th order u x w x n x ... x n tensor A and an m-th order w x v x n x ... x n tensor B. Note that v must not exceed n. The resulting C is an m-th order u x v x n x ... x n tensor whose entries are defined as: 
c_{i_1i_2 ... i_m}=sum_{j=1}^w a_{i_1ji_2 ... i_{m-1}}b_{ji_2 ... i_m}.

The function C=bpowe(A,k) computes the k-th power A^k of an m-th order u x u x n x ... x n tensor A. Note that u must not exceed n. This power is defined recursively by 
A^k=bprode(A^{k-1},A), k=1,2,3,...,
with A^0 being defined to be the m-th order u x u x n x ... x n identity tensor.