Enumeration of flattened kk-Stirling permutations with respect to descents

A $k$-Stirling permutation of order $n$ is said to be "flattened" if the leading terms of its increasing runs are in ascending order. We show that flattened $k$-Stirling permutations of order $n+1$ are in bijection correspondence with a colored variant of type $B$ set partitions of $[-n,n]$, introduced by D.G.L. Wang. Using the theory of weighted labelled structures, we give the exponential generating functions of their cardinality and their descent enumerating polynomials. We also provide enumerative formulae for the number of flattened $k$-Stirling permutations of order $n$ with small number of descents and the number of flattened Stirling permutations with maximum number of descents.Comment: 22 pages, 1 table. Comments are welcom

Obstructions in Security-Aware Business Processes

This Open Access book explores the dilemma-like stalemate between security and regulatory compliance in business processes on the one hand and business continuity and governance on the other. The growing number of regulations, e.g., on information security, data protection, or privacy, implemented in increasingly digitized businesses can have an obstructive effect on the automated execution of business processes. Such security-related obstructions can particularly occur when an access control-based implementation of regulations blocks the execution of business processes. By handling obstructions, security in business processes is supposed to be improved. For this, the book presents a framework that allows the comprehensive analysis, detection, and handling of obstructions in a security-sensitive way. Thereby, methods based on common organizational security policies, process models, and logs are proposed. The Petri net-based modeling and related semantic and language-based research, as well as the analysis of event data and machine learning methods finally lead to the development of algorithms and experiments that can detect and resolve obstructions and are reproducible with the provided software