Related papers: Reduced words for clans
Correlation clustering is a technique for aggregating data based on qualitative information about which pairs of objects are labeled 'similar' or 'dissimilar.' Because the optimization problem is NP-hard, much of the previous literature…
We investigate Bruhat-Tits buildings and their compactifications by means of Berkovich analytic geometry over complete non-Archimedean fields. For every reductive group G over a suitable non-Archimedean field k we define a map from the…
We define a partition of a reductive group into finitely many subsets, refining the partition of the group into strata. We state some conjectural properties of these subsets (called substrata) and verify them in some examples.
Indexed languages are a classical notion in formal language theory, which has attracted attention in recent decades due to its role in higher-order model checking: They are precisely the languages accepted by order-2 pushdown automata. The…
Every reduced ring $R$ has a natural partial order defined by $a\le b$ if $a^2=ab$; it generalizes the natural order on a boolean ring. The article examines when $R$ is a lower semi-lattice in this order with examples drawn from weakly Baer…
Special matchings are purely combinatorial objects associated with a partially ordered set, which have applications in Coxeter group theory. We provide an explicit characterization and a complete classification of all special matchings of…
Previous work has shown that the disarray (or displacement) of an (affine) (signed) permutation is bounded in terms of its Coxeter length. Here, we characterize the permutations for which the bound is sharp in two ways: in terms of a…
Vector space representations of words capture many aspects of word similarity, but such methods tend to make vector spaces in which antonyms (as well as synonyms) are close to each other. We present a new signed spectral normalized graph…
Conjunctive table algebras are introduced and axiomatically characterized. A conjunctive table algebra is a variant of SPJR algebra (a weaker form of relational algebra), which corresponds to conjunctive queries with equality. The table…
Several general properties, concerning reduction algebras - rings of definition and algorithmic efficiency of the set of ordering relations - are discussed. For the reduction algebras, related to the diagonal embedding of the Lie algebra…
We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical…
Indexed languages are interesting in computational linguistics because they are the least class of languages in the Chomsky hierarchy that has not been shown not to be adequate to describe the string set of natural language sentences. We…
We study the appearance of notable interval structures -- lattices, modular lattices, distributive lattices, and boolean lattices -- in both the Bruhat and weak orders of Coxeter groups. We collect and expand upon known results for…
We review Stanley's seminal work on the number of reduced words of the longest element of the symmetric group and his Stanley symmetric functions. We shed new light on this by giving a crystal theoretic interpretation in terms of decreasing…
We study parabolic double cosets in a Coxeter system by decomposing them into atom(ic coset)s, a generalization of simple reflections introduced in a joint work with Elias, Libedinsky, Patimo. We define and classify braid relations between…
The reduced expressions for a given element $w$ of a Coxeter group $(W, S)$ can be regarded as the vertices of a directed graph $\mathcal{R}(w)$; its arcs correspond to the braid moves. Specifically, an arc goes from a reduced expression…
We characterize relatively norm compact sets in the regular $C^*$-algebra of finitely generated Coxeter groups using a geometrically defined positive semigroup acting on the algebra.
Let G be the group of rational points of a semisimple algebraic group of rank 1 over a nonarchimedean local field. We improve upon Lubotzky's analysis of graphs of groups describing the action of lattices in G on its Bruhat-Tits tree…
We define a class of partial orders on a Coxeter group associated with sets of reflections. In special cases, these lie between the left weak order and the Bruhat order. We prove that these posets are graded by the length function and that…
Dictionaries are inherently circular in nature. A given word is linked to a set of alternative words (the definition) which in turn point to further descendants. Iterating through definitions in this way, one typically finds that…