Related papers: Chains of modular elements and shellability
For an orthogonal modular variety, we construct a complex which is defined in terms of lattices and elliptic modular forms, which resembles the Gersten complex in Milnor K-theory, and which has a morphism to the Gersten complex of the…
We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived infinity-category…
Defining P* to be the complete lattice of upsets (ordered by reverse inclusion) of a poset P we give necessary and sufficient conditions on a subset S of P* for P to admit a meet-completion e from P to Q where e preserves the infimum of an…
We prove that for all $d \geq 1$ a shellable $d$-dimensional simplicial complex with at most $d+3$ vertices is extendably shellable. The proof involves considering the structure of `exposed' edges in chordal graphs as well as a connection…
By enumerating all sequences of length 20, we study the designability of structures in a two-dimensional Hydrophobic-Polar (HP) lattice model in a wide range of inter-monomer interaction parameters. We find that although the histogram of…
We give a simple characterization of the highest weight vertices in the crystal graph of the level l Fock spaces. This characterization is based on the notion of totally periodic symbols viewed as affine analogues of reverse lattice words…
We recently introduced a notion of tilings of geometric realizations of finite relative simplicial complexes and related those tilings to the discrete Morse theory of R. Forman, especially when they have the property of being shellable, a…
We completely determine all semigroup [epigroup] varieties that are cancellable elements of the lattice of all semigroup [respectively epigroup] varieties.
We establish the essential normality of a large new class of homogeneous submodules of the finite rank d-shift Hilbert module. The main idea is a notion of essential decomposability that determines when an arbitrary submodule can be…
We consider the problem of finding lower bounds on the number of unlabeled $n$-element lattices in some lattice family. We show that if the family is closed under vertical sum, exponential lower bounds can be obtained from vertical sums of…
We introduce pseudo-Gorenstein rings and characterize those Hibi rings attached to a finite distributive lattice L which are pseudo-Gorenstein. The characterization is given in terms of the poset of join-irreducible elements of L. We also…
Let $M$ be a smooth algebraic variety of dimension $2(p+q)$ with an algebraic symplectic form and a compatible deformation quantization $\mathcal{O}_h$ of the structure sheaf. Consider a smooth coisotropic subvariety $j: Y \to M$ of…
Rival and Zaguia showed that the antichain cutsets of a finite Boolean lattice are exactly the level sets. We show that a similar characterization of antichain cutsets holds for any strongly connected poset of locally finite height. As a…
We settle the complexity of satisfiability, finite-state satisfiability, and model-checking for several fragments of second-order HyperLTL, which extends HyperLTL with quantification over sets of traces: they are all in the analytical…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
We completely determine all semigroup varieties satisfiyng a permutational identity of length 3 that are cancellable elements of the lattice of all semigroup varieties. Using this result, we provide a series of new examples of semigroup…
We give a new proof of the fact that finite bipartite graphs cannot be axiomatized by finitely many first-order sentences among FINITE graphs. (This fact is a consequence of a general theorem proved by L. Ham and M. Jackson, and the…
In this note, I find a new property of the congruence lattice, Con$L$, of an SPS lattice $L$ (slim, planar, semimodular, where "slim" is the absence of~$\mathsf M_3$ sublattices) with more than $2$ elements: \emph{there are at least two…
Using the concept of a cohesive module defined by Block, we use the theory of superconnections in the sense of Quillen to construct natural superconnections on Hermitian cohesive modules. By the Chern-Weil construction, we obtain…
We apply the homomorphism complex construction to partially ordered sets, introducing a new topological construction based on the set of maximal chains in a graded poset. Our primary objects of study are distributive lattices, with special…