Results 1 to 10 of about 351,610 (104)
The Varchenko determinant of an oriented matroid [PDF]
Transactions on Combinatorics, 2021 Varchenko introduced in 1993 a distance function on the chambers of a hyperplane arrangement that gave rise to a determinant whose entry in position $(C, D)$ is the distance between the chambers $C$ and $D$, and computed that determinant. In 2017, Aguiar
Hery Randriamaro
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Hyperfactord of Shi arrangement Sh(A2) and Sh(A3)
Al-Mustansiriyah Journal of Science, 2022 In this paper, we introduce the region and the faces poset of shi arrangement that J. Y. Shi firstly introduced it. This is an affine arrangement, each of whose hyperplane is parallel to some"hyperplane of Coxeter arrangement"(Braid arrangement), the ...
Alaa A. A. Al-Mujmaey +1 more
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Counting Shi regions with a fixed separating wall [PDF]
Discrete Mathematics & Theoretical Computer Science, 2011 Athanasiadis introduced separating walls for a region in the extended Shi arrangement and used them to generalize the Narayana numbers. In this paper, we fix a hyperplane in the extended Shi arrangement for type A and calculate the number of dominant ...
Susanna Fishel +2 more
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Affine and toric arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We extend the Billera―Ehrenborg―Readdy map between the intersection lattice and face lattice of a central hyperplane arrangement to affine and toric hyperplane arrangements.
Richard Ehrenborg +2 more
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IET Networks, EarlyView., 2022 Abstract Sensor technology advancements have provided a viable solution to fight COVID and to develop healthcare systems based on Internet of Things (IoTs). In this study, image processing and Artificial Intelligence (AI) are used to improve the IoT framework.
Noor M Allayla +2 more
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The arithmetic Tutte polynomials of the classical root systems [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the
Federico Ardila +2 more
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Wonderful compactifications and rational curves with cyclic action
Forum of Mathematics, Sigma, 2023 We prove that the moduli space of rational curves with cyclic action, constructed in our previous work, is realizable as a wonderful compactification of the complement of a hyperplane arrangement in a product of projective spaces.
Emily Clader +3 more
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The freeness of Ish arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 The Ish arrangement was introduced by Armstrong to give a new interpretation of the $q; t$-Catalan numbers of Garsia and Haiman. Armstrong and Rhoades showed that there are some striking similarities between the Shi arrangement and the Ish arrangement ...
Takuro Abe +2 more
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Gallery Posets of Supersolvable Arrangements [PDF]
Discrete Mathematics & Theoretical Computer Science, 2014 We introduce a poset structure on the reduced galleries in a supersolvable arrangement of hyperplanes. In particular, for Coxeter groups of type A or B, we construct a poset of reduced words for the longest element whose Hasse diagram is the graph of ...
Thomas McConville
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From Bruhat intervals to intersection lattices and a conjecture of Postnikov [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 We prove the conjecture of A. Postnikov that ($\mathrm{A}$) the number of regions in the inversion hyperplane arrangement associated with a permutation $w \in \mathfrak{S}_n$ is at most the number of elements below $w$ in the Bruhat order, and ($\mathrm ...
Axel Hultman +3 more
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