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Interval Posets of Permutations
The interval poset of a permutation catalogues the intervals that appear in its one-line notation, according to set inclusion. We study this poset,...
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Geometric Realizations of Tamari Interval Lattices Via Cubic Coordinates
We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with...
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Dimension of Restricted Classes of Interval Orders
Rabinovitch showed in 1978 that the interval orders having a representation consisting of only closed unit intervals have order dimension at most
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The Canonical Complex of the Weak Order
We define and study the canonical complex of a finite semidistributive lattice L . It is the simplicial complex on the join or meet irreducible...
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The Dimension of Divisibility Orders and Multiset Posets
The Dushnik–Miller dimension of a poset P is the least d for which P can be embedded into a product of d chains. Lewis and Souza isibility order on...
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Special idempotents and projections
We define, for any special matching of a finite graded poset, an idempotent, regressive and order preserving function. We consider the monoid...
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On Dually-CPT and Strongly-CPT Posets
A poset is a containment of paths in a tree (CPT) if it admits a representation by containment where each element of the poset is represented by a...
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A Proof of the Alternate Thomassé Conjecture for Countable N-Free Posets
An N -free poset is a poset whose comparability graph does not embed an induced path with four vertices. We use the well-quasi-order property of the...
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The Newton polytope and Lorentzian property of chromatic symmetric functions
Chromatic symmetric functions are well-studied symmetric functions in algebraic combinatorics that generalize the chromatic polynomial and are...
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From the Lattice of Torsion Classes to the Posets of Wide Subcategories and ICE-closed Subcategories
In this paper, we compute the posets of wide subcategories and ICE-closed subcategories from the lattice of torsion classes in an abelian length...
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Lattice Theory
The first symbols are very much used, when the elements are sets, but they are different to read, easy to confuse and lack standard verbal...
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Characteristic Polynomials of the Weak Order on Classical and Affine Coxeter Groups
We find a simple product formula for the characteristic polynomial of the permutations with a fixed descent set under the weak order. As a corollary...
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The isomorphism problem for ideal class monoids of numerical semigroups
From any poset isomorphic to the poset of gaps of a numerical semigroup S with the order induced by S , one can recover S . As an application, we prove...
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The Type B Permutohedron and the Poset of Intervals as a Tchebyshev Transform
We show that the order complex of the poset of nonempty intervals, ordered by inclusion, is a Tchebyshev triangulation of the order complex of the...
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Variations of Statement, Variations of Strength. The Case of the Rival–Sands Theorems
The paper surveys results obtained mainly by the author with A. Marcone, P. Shafer, and G. Soldà centered around two theorems due to I. Rival and B....
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A Large Class of Conjecturally Stable Chromatic Symmetric Functions
The theory of stable and Lorentzian polynomials has recently found a number of successes in a variety of research areas including combinatorics,...
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Well-quasi-ordering and Embeddability of Relational Structures
At the end of the forties, Fraïssé, following Cantor, Hausdorff and Sierpinski, highlighted the role of the embeddability quasi-order in the theory...
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Poincaré duality for generalized persistence diagrams of (co)filtrations
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express...
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