The random utility model is known to be unidentified, but there are times when the admits a unique representation. We offer two characterizations for existence of Our first characterization puts conditions on graphical representation data set. Non-uniqueness arises multiple inflows can assigned outflows this graph. second provides direct test uniqueness given also show that support identified i...

We introduce a model for random chain complexes over finite field. The randomness in our complex comes from choosing the entries matrices that represent boundary maps uniformly \(\mathbb {F}_q\), conditioned on ensuring composition of consecutive is zero map. then investigate combinatorial and homological properties this complex.