Phylogenetic varieties related to equivariant substitution models have been studied largely in the last years. One of the main objectives has been finding a set of generators of the ideal of these varieties, but this has not yet been achieved in some cases (for example, for the general Markov model this involves the open “salmon conjecture”, see [2]) and it is not clear how to use all generator...

In this article we offer group-theoretic, field-theoretic, and topological interpretations of the Gaussian binomial coefficients their sum. For a finite p-group G rank n, show that coefficient (nk)p is number subgroups are minimally expressible as an intersection n – k maximal G, sum precisely either or G. We provide field-theoretic interpretation these quantities through lens Galois theory inv...

We introduce a notion of weak intersection number of a collection of sets, modifying the notion of intersection number due to J.L. Kelley, and obtain an analogue of Kelley’s characterization of Boolean algebras which support a finitely additive strictly positive measure. We also consider graph-theoretic reformulations of the notions of intersection number and weak intersection number. Kelley [4...

Finite state methods for natural language processing often require the construction and the intersection of several automata. In this paper we investigate the question of determining the best order in which these intersections should be performed. We take as an example lexical disambiguation in polarity grammars. We show that there is no efficient way to minimize the state complexity of these i...

The seminal complete intersection theorem of Ahlswede and Khachatrian gives the maximum cardinality of a k-uniform t-intersecting family on n points, and describes all optimal families for t ≥ 2. We extend this theorem to the weighted setting, in which we consider unconstrained families. The goal in this setting is to maximize the μp measure of the family, where the measure μp is given by μp(A)...

betweenness, geometry, lines, polar coordinates, trilinear coordinates We consider straight line drawings. From a graph theoretic point of view these are plane graphs with a set of preferred paths. This graph is expressed in geometric terms through the consideration of the betweenness of the points of intersection along each of the lines. If we fix a reference system for polar coordinates, we c...

Consider the discrete conditional independence model M given by {X1 ⊥ X2 | X3, X1 ⊥ X3 | X2}. The intersection axiom for conditional independence can be applied with the statements of M as premises to derive the conclusion X1 ⊥ (X2, X3). But the independence axiom only holds in general when X is in the interior of the probability simplex, and it’s a natural question to ask what can be inferred ...

We develop the theory of coregular sequences and codepth for modules that need not be finitely generated or artinian over a Noetherian ring. use this to give new version theorem Hellus characterizing set-theoretic complete intersections in terms local cohomology modules. also define quasi-cyclic as increasing unions cyclic modules, show at least two are quasi-cyclic. then focus our attention on...

In this work we present a proof-theoretical justification for the intersection type assignment system (IT) by means of the logical system Intersection Synchronous Logic (ISL). ISL builds classes of equivalent deductions of the implicative and conjunctive fragment of the intuitionistic logic (NJ). ISL results from decomposing intuitionistic conjunction into two connectives: a synchronous conjunc...