Search Results - "Brignall, Robert"

2\times 2$ monotone grid classes are finitely based by Albert, Michael, Brignall, Robert

“…In this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations…”
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Labelled Well-Quasi-Order in Juxtapositions of Permutation Classes by Brignall, Robert

“…The juxtaposition of permutation classes $\mathcal{C}$ and $\mathcal{D}$ is the class of all permutations formed by concatenations $\sigma\tau$, such that…”
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Well‐quasi‐ordering and finite distinguishing number by Atminas, Aistis, Brignall, Robert

“…Balogh, Bollobás and Weinreich showed that a parameter that has since been termed the distinguishing number can be used to identify a jump in the possible…”
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Labelled well-quasi-order for permutation classes by Brignall, Robert, Vatter, Vincent

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Grid classes and partial well order by Brignall, Robert

“…We prove necessary and sufficient conditions on a family of (generalised) gridding matrices to determine when the corresponding permutation classes are…”
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A Counterexample Regarding Labelled Well-Quasi-Ordering by Brignall, Robert, Engen, Michael, Vatter, Vincent

“…Korpelainen, Lozin, and Razgon conjectured that a hereditary property of graphs which is well-quasi-ordered by the induced subgraph order and defined by only…”
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Uncountably Many Minimal Hereditary Classes of Graphs of Unbounded Clique-Width by Brignall, Robert, Cocks, Daniel

“…Given an infinite word over the alphabet $\{0,1,2,3\}$, we define a class of bipartite hereditary graphs $\mathcal{G}^\alpha$, and show that…”
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Combinatorial Specifications for Juxtapositions of Permutation Classes by Brignall, Robert, Sliačan, Jakub

“…We show that, given a suitable combinatorial specification for a permutation class $\mathcal{C}$, one can obtain a specification for the juxtaposition (on…”
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Linear Clique‐Width for Hereditary Classes of Cographs by Brignall, Robert, Korpelainen, Nicholas, Vatter, Vincent

“…The class of cographs is known to have unbounded linear clique‐width. We prove that a hereditary class of cographs has bounded linear clique‐width if and only…”
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Juxtaposing Catalan Permutation Classes with Monotone Ones by Brignall, Robert, Sliačan, Jakub

“…This paper enumerates all juxtaposition classes of the form "$\mathrm{Av}(abc)$ next to $\mathrm{Av}(xy)$", where $abc$ is a permutation of length three and…”
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Labelled well-quasi-order in juxtapositions of permutation classes by Brignall, Robert

“…The juxtaposition of permutation classes $\mathcal{C}$ and $\mathcal{D}$ is the class of all permutations formed by concatenations $\sigma\tau$, such that…”
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Bichain graphs: Geometric model and universal graphs by Brignall, Robert, Lozin, Vadim V., Stacho, Juraj

“…Bichain graphs form a bipartite analog of split permutation graphs, also known as split graphs of Dilworth number 2. Unlike graphs of Dilworth number 1 that…”
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Enumerating indices of Schubert varieties defined by inclusions by Albert, Michael H., Brignall, Robert

“…By extending the notion of grid classes to include infinite grids, we establish a structural characterisation of the simple permutations in…”
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2×22×2 monotone grid classes are finitely based by Albert, Michael, Brignall, Robert

“…In this note, we prove that all 2×22×2 monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This…”
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Staircases, dominoes, and the growth rate of 1324-avoiders by Bevan, David, Brignall, Robert, Price, Andrew Elvey, Pantone, Jay

“…We establish a lower bound of 10.271 for the growth rate of the permutations avoiding 1324, and an upper bound of 13.5. This is done by first finding the…”
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ZEROS OF THE MÖBIUS FUNCTION OF PERMUTATIONS by Brignall, Robert, Jelínek, Vít, Kynčl, Jan, Marchant, David

“…We show that if a permutation $\unicode[STIX]{x1D70B}$ contains two intervals of length 2, where one interval is an ascent and the other a descent, then the…”
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A framework for minimal hereditary classes of graphs of unbounded clique-width by Brignall, Robert, Cocks, Daniel

“…SIAM J. Disc. Math. Vol. 37, Iss. 4 (2023) We create a framework for hereditary graph classes $\mathcal{G}^\delta$ built on a two-dimensional grid of vertices…”
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Well-Quasi-Order for Permutation Graphs Omitting a Path and a Clique by Atminas, Aistis, Brignall, Robert, Korpelainen, Nicholas, Lozin, Vadim, Vatter, Vincent

“…We consider well-quasi-order for classes of permutation graphs which omit both a path and a clique. Our principle result is that the class of permutation…”
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Uncountably many enumerations of well-quasi-ordered permutation classes by Brignall, Robert, Vatter, Vincent

“…We construct an uncountable family of well-quasi-ordered permutation classes, each with a distinct enumeration sequence. This disproves a widely-held…”
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Simple permutations: Decidability and unavoidable substructures by Brignall, Robert, Ruškuc, Nik, Vatter, Vincent

“…We prove that it is decidable whether a finitely based permutation class contains infinitely many simple permutations, and establish an unavoidable…”
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