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An exploration of combinatorial testing-based approaches to fault localization for explainable AI
We briefly review properties of explainable AI proposed by various researchers. We take a structural approach to the problem of explainable AI,...
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Representability of Ramsey Relation Algebras
We obtain representations for relation algebras corresponding to certain edge colourings of complete graphs. Suitable colourings are obtained for the...
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A combinatorial approach to binary positional number systems
Although the representation of the real numbers in terms of a base and a set of digits has a long history, new questions arise even in the binary...
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Transforms and Minors for Binary Functions
We introduce a family of transforms that extends graph- and matroid-theoretic duality, and includes trinities and so on. Associated with each such...
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Quaternary Golay sequence pairs II: odd length
A 4-phase Golay sequence pair of length s ≡ 5 (mod 8) is constructed from a Barker sequence of the same length whose even-indexed elements are...
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Quaternary Golay sequence pairs I: even length
The origin of all 4-phase Golay sequences and Golay sequence pairs of even length at most 26 is explained. The principal techniques are the...
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An introduction to balanced sequential arrays on the square grid
Plants grown in large numbers for commercial purposes are usually set out on a regular grid, triangular, square or hexagonal, or possibly a...
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On the maximum number of points at least one unit away from each other in the unit n-cube
We present a very short survey of known results and many new estimates and results on the maximum number of points that can be chosen in the n -dimensi...
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What is a design? How should we classify them?
Design theory crosses the boundary between mathematics and statistics, and includes a wide range of disparate types of design. In this paper we...
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A Characterization of Mixed Branching Greedoids
Branching greedoids have been defined and characterized for both directed and undirected rooted graphs. Such greedoids can be extended to rooted...
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Fusion Relation in Products of Association Schemes
Fusion relations between the association schemes obtained by direct product and wreath product are established via a study of their matrix...
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Constructions for higher dimensional perfect multifactors
Perfect maps, factors and multifactors can be viewed as higher dimensional analogues of de Bruijn cycles and factored versions of these cycles. We...
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On the Support Size of Null Designs of Finite Ranked Posets
-designs of the lattice of subspaces of a vector space over a finite field. The lower bound we find gives the tight bound for many important posets...
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Bases for Splines on a Subdivided Domain
Let S r (Δ) be the module of all splines of smoothness r on the rectilinear partition Δ which subdivides some domain D. Further, let S r (Γ) be the...
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There are uncountably many universal topological planes
We prove the existence of uncountably many nonisomorphic topological projective planes, each ‘universal’ in the sense that it contains an isomorphic...
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