A Bruhat order for the class of -matrices with row sum vector and column sum vector .
A class of -preduals which are isomorphic to quotients of
For every countable ordinal α, we construct an -predual which is isometric to a subspace of and isomorphic to a quotient of . However, is not isomorphic to a subspace of .
A continuum of totally incomparable hereditarily indecomposable Banach spaces
A family is constructed of cardinality equal to the continuum, whose members are totally incomparable hereditarily indecomposable Banach spaces.
A finite word poset.
A metric on a system of ordered sets
In [3] a metric on a system of isomorphism classes of ordered sets was defined. In this paper we define another metric on the same system and investigate some of its properties. Our approach is motivated by a problem from practice.
A note on Möbius inversion over power set lattices
In this paper, we establish a theorem on Möbius inversion over power set lattices which strongly generalizes an early result of Whitney on graph colouring.
A relative Laplacian spectral recursion.
A remark on growth relation.
A sharp bound for the reconstruction of partitions.
Affine permutations of type .
An analogue of covering space theory for ranked posets.
An analysis of GCD and LCM matrices via the -factorization.
An infinite antichain of permutations.
Antichains in the homomorphism order of graphs
Let and , respectively, denote the partially ordered sets of homomorphism classes of finite undirected and directed graphs, respectively, both ordered by the homomorphism relation. Order theoretic properties of both have been studied extensively, and have interesting connections to familiar graph properties and parameters. In particular, the notion of a duality is closely related to the idea of splitting a maximal antichain. We construct both splitting and non-splitting infinite maximal antichains...
Antichains of multisets.
Bound graph polysemy.
Bound quivers of three-separate stratified posets, their Galois coverings and socle projective representations
A class of stratified posets is investigated and their incidence algebras are studied in connection with a class of non-shurian vector space categories. Under some assumptions on we associate with a bound quiver (Q, Ω) in such a way that . We show that the fundamental group of (Q, Ω) is the free group with two free generators if is rib-convex. In this case the universal Galois covering of (Q, Ω) is described. If in addition is three-partite a fundamental domain of this covering is...
Bruhat intervals, polyhedral cones and Kazhdan-Lusztig-Stanley polynomials.
Cambrian fans
For a finite Coxeter group and a Coxeter element of ; the -Cambrian fan is a coarsening of the fan defined by the reflecting hyperplanes of . Its maximal cones are naturally indexed by the -sortable elements of . The main result of this paper is that the known bijection cl between -sortable elements and -clusters induces a combinatorial isomorphism of fans. In particular, the -Cambrian fan is combinatorially isomorphic to the normal fan of the generalized associahedron for . The rays...
Chain polynomials of distributive lattices are 75% unimodal.