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Despite Information and Communication Technologies (ICT) have reduced the information asymmetry and increased the degree of interorganizational collaboration, the companies participating a supply chain are less inclined to share data when information is sensible and partners cannot be fully trusted. In such a context, Blockchain is a decentralized certificate authority that may provide economic and operational benefits but companies operating in a supply chain claim to have little knowledge about Blockchain due to its novelty and to the lack of use cases and application studies. In this work, a software connector has been designed and developed to connect an Ethereum-like blockchain with the enterprises' information systems to allow companies to share information with their partners with different levels of visibility and to check data authenticity, integrity and invariability over time through the blockchain, thus building trust. In order to explore the potential of deploying the blockchain in a supply chain, a simulation model has been developed to recreate the supply chain operations and integrated with the blockchain through the same software connector to carry out a scenario statistical analysis. Application results shows how blockchain technology is a convenient instrument to overcome collaboration and trust issues in a supply chain, to increase the supply chain overall performance, to minimize the negative consequences of information asymmetry over the echelons of a supply chain but also to discourage companies from any misconduct (e.g. counterfeiting data or low data accuracy)., Comment: 13 pages, 15 figures, 10 tables

Literature considers under the name \emph{unimaginable numbers} any positive integer going beyond any physical application, with this being more of a vague description of what we are talking about rather than an actual mathematical definition. This simply means that research in this topic must always consider shortened representations, usually involving \emph{recursion}, to even being able to describe such numbers.\par\medskip One of the most known methodologies to conceive such numbers is using \emph{hyperoperations}, that is a sequence of binary functions defined recursively starting from the usual chain: addition - multiplication - exponentiation. The most important notations to represent such hyperoperations have been considered by Knuth, Goodstein, Ackermann and Conway as described in this work's introduction.\par\medskip Within this work we will give an axiomatic set for this topic, and then try to find on one hand other ways to represent unimaginable numbers, as well as on the other hand applications to computer science, where the algorithmic nature of representations and the increased computation capabilities of computers give the perfect field to develop further the topic.\par\medskip After the introduction, we will give axioms and generalizations for the up-arrow notation; in the subsequent section we consider a representation via rooted trees of the \emph{hereditary base-$n$ notation} involved in Goodstein's theorem, which can be used efficiently to represent some defective unimaginable numbers, and in the last section we will analyse some methods to compare big numbers, proving specifically a theorem about approximation using scientific notation., Comment: 15 pages, 5 figures. Related to the conference "The First Symposium of the International Pythagorean School -- da Pitagora a Sch\"utzenberger: numeri inimmaginabil\^i\^i\^i"