Sensitivity diagnostics has recently been put high on the agenda of methodological research into Qualitative Comparative Analysis (QCA). Existing studies in this area rely on the technique of exhaustive enumeration, and the vast majority of works examine the reactivity of QCA either only to alterations in discretionary parameter values or only to data quality. In this article, we introduce the ...

Some constraint problems have a combinatorial structure where the constraints allow the sequence of variables to be rotated (necklaces), if not also the domain values to be permuted (unlabelled necklaces), without getting an essentially different solution. We bring together the fields of combinatorial enumeration, where efficient algorithms have been designed for (special cases of) some of thes...

We provide bivariate asymptotics for the poly-Bernoulli numbers, a combinatorial array that enumerates lonesum matrices, using methods of Analytic Combinatorics in Several Variables (ACSV). For diagonal asymptotic (i.e., special case square matrices) we present an alternative proof based on Parseval's identity. In addition, application Algebraic Statistics ML-degree multinomial missing data pro...

We propose a recursive method for the computation of cumulants self-exciting point processes Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement higher-order in comparison with existing methods differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and al...

Kashiwara and Saito have defined a crystal structure on the set of irreducible components of Lusztig’s quiver varieties. This gives a geometric realization of the crystal graph of the lower half of the quantum group associated to a simply-laced Kac-Moody algebra. Using an enumeration of the irreducible components of Lusztig’s quiver varieties in finite and affine type A by combinatorial data, w...

We consider a partially asymmetric exclusion process (PASEP) on a finite number of sites with open and directed boundary conditions. Its partition function was calculated by Blythe, Evans, Colaiori, and Essler. It is known to be a generating function of permutation tableaux by the combinatorial interpretation of Corteel and Williams. We prove bijectively two new combinatorial interpretations. T...

The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P-irreducible triangulation. In addition we present constraints upon the combinatorial structure of such a triangulation that can be deduced from its face...

Integer programming algorithms based on the ordered enumeration method are described. Combining dynamic programming and branch and bound ideas in one efficient computational process, S. S. Lebedev implemented his method for solving integer linear programming problems in 1968. A number of ordered enumeration algorithms were developed since the 1970's. The author has been actively involved in thi...

Many real-world problems require the enumeration of all solutions of combinatorial search problems, even though this is often infeasible in practice. However, not always all parts of a solution are needed. We are thus interested in projecting solutions to a restricted vocabulary. Yet, the adaption of Boolean constraint solving algorithms turns out to be non-obvious provided one wants a repetiti...