Based on a recent improvement of the inclusion-exclusion principle, we present a new approach to network reliability problems. In particular, we give a new proof of a result of Shier, which expresses the reliability of a network as an alternating sum over chains in a semilattice, and a new proof of a result of Provan and Ball, which provides an algorithm for computing network reliability in pse...

Given a set N with n elements and a family F of subsets, we show how to partition N into k such subsets in 2nnO(1) time. We also consider variations of this problem where the subsets may overlap or are weighted, and we solve the decision, counting, summation, and optimisation versions of these problems. Our algorithms are based on the principle of inclusion–exclusion and the zeta transform. In ...

We prove that an inclusion-exclusion inspired expression of Schubert polynomials permutations avoid the patterns 1432 and 1423 is nonnegative. Our theorem implies a partial affirmative answer to recent conjecture Yibo Gao about principal specializations polynomials. propose general framework for finding all permutations.

Abstract Through ethnographic fieldwork conducted in 2020–2021, this paper investigates how people experiencing poverty and social exclusion process their collective in-group/ out-group identity as the urban ‘others’ faith-based food assistance Finland. By building on concept of employing narrative construction, analysis shows that not only does perceived function a stigmatizing self-category s...

The paper introduces an exclusion/inclusion fuzzy classification neural network. The network is based on our GFMM [3] and it allows for two distinct types of hyperboxes to be created: inclusion hyperboxes that correspond directly to those considered in GFMM, and exclusion hyperboxes that represent contentious areas of the pattern space. The subtraction of the exclusion hyperboxes from the inclu...

Taking a combinatorial point of view on cyclotomic polynomials leads to a larger class of polynomials we shall call the inclusion-exclusion polynomials. This gives a more appropriate setting for certain types of questions about the coefficients of these polynomials. After establishing some basic properties of inclusion-exclusion polynomials we turn to a detailed study of the structure of ternar...

Using Maple, we implement a SAT solver based on the principle of inclusion-exclusion and the Bonferroni inequalities. Using randomly generated input, we investigate the performance of our solver as a function of the number of variables and number of clauses. We also test it against Maple’s built-in tautology procedure. Finally, we implement the Lovász local lemma with Maple and discuss its appl...