Results 91 to 100 of about 4,538 (218)
The Electronic Journal of Combinatorics, 2005 Macaulay posets are posets for which there is an analogue of the classical Kruskal-Katona theorem for finite sets. These posets are of great importance in many branches of combinatorics and have numerous applications. We survey mostly new and also some old results on Macaulay posets, where the intention is to present them as pieces of a general theory.
Bezrukov, Sergei L., Leck, Uwe
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The Poset of Proper Divisibility [PDF]
SIAM Journal on Discrete Mathematics, 2017 We study the partially ordered set $P(a_1,\ldots, a_n)$ of all multidegrees $(b_1,\dots,b_n)$ of monomials $x_1^{b_1}\cdots x_n^{b_n}$ which properly divide $x_1^{a_1}\cdots x_n^{a_n}$. We prove that the order complex $Δ(P(a_1,\dots,a_n))$ of $P(a_1,\ldots a_n)$ is (non-pure) shellable, by showing that the order dual of $P(a_1,\ldots,a_n)$ is $\mathrm ...
Bolognini, Davide +4 more
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Attribute Implication Bases From Galois Connection Structures
Mathematical Methods in the Applied Sciences, Volume 49, Issue 4, Page 2729-2753, 15 March 2026.ABSTRACT Modeling knowledge systems by determining relationships among key variables have been and currently is a fundamental and nontrivial challenge in real‐world scenarios. Many approaches have been developed to reach this goal, but many of them are heuristic and require of alternative procedures to provide robust and tractable rules.
M. Eugenia Cornejo +2 more
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The saturation number for the diamond is linear
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract For a fixed poset P$\mathcal {P}$ we say that a family F⊆P([n])$\mathcal {F}\subseteq \mathcal {P}([n])$ is P$\mathcal {P}$‐saturated if it does not contain an induced copy of P$\mathcal {P}$, but whenever we add a new set to F$\mathcal {F}$, we form an induced copy of P$\mathcal {P}$.
Maria‐Romina Ivan, Sean Jaffe
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Modeling Poset Convex Subsets [PDF]
, 2015 A subset S of a poset (partially ordered set) is convex if and only if S contains every poset element which is between any two elements in S. Poset convex subsets arise in applications that involve precedence constraints, such as in project scheduling ...
Wolsey, Laurence, Queyranne, Maurice
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On posets with isomorphic interval posets [PDF]
Czechoslovak Mathematical Journal, 1999 Let \((A,\leq)\) be a partially ordered set (poset). By an interval of \(A\) is meant a nonempty set \(\{x\in A; a\leq x \leq b\}\), for some \(a,b\in A\), \(a\leq b\). Denote by \(\operatorname {Int} A\) the poset of all intervals of \(A\) ordered by set inclusion.
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Fixed‐point posets of groups and Euler characteristics
Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.Abstract Suppose that G$G$ is a group and Ω$\Omega$ is a G$G$‐set. For X$\mathcal {X}$ a set of subgroups of G$G$, we introduce the fixed‐point poset XΩ$\mathcal {X}_{\Omega }$. A variety of results concerning XΩ$\mathcal {X}_{\Omega }$ are proved as, for example, in the case when p$p$ is a prime and X$\mathcal {X}$ is a non‐empty set of finite non ...
Peter Rowley
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The Möbius function of the consecutive pattern poset
, 2011 An occurrence of a consecutive permutation pattern p in a permutation π is a segment of consecutive letters of π whose values appear in the same order of size as the letters in p.
Steingrimsson, E. +2 more
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Discrete Mathematics, 1981 AbstractMany of the well-known selection and sorting problems can be understood as the production of certain partial orders, using binary comparisons. The paper discusses the complexity of the production of arbitrary posets all of a given size n (on a totally ordered ground-set).
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Assembly of constructible factorization algebras
Journal of Topology, Volume 19, Issue 1, March 2026.Abstract We provide a toolbox of extension, gluing, and assembly techniques for factorization algebras. Using these tools, we fill various gaps in the literature on factorization algebras on stratified manifolds, the main one being that constructible factorization algebras form a sheaf of symmetric monoidal ∞$\infty$‐categories.
Eilind Karlsson +2 more
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