Related papers: Symbolic powers, set-theoretic complete intersecti…
In this paper, we find a criterion to answer when the second symbolic and ordinary powers of the edge ideal of a 3-partite hypergraph are equal. Also, we give the formula to compute the Waldschmidt constant of the path ideals of a cycle.
Configurations of points defined by complex reflection groups have attracted a lot of attention recently in several directions of research, e.g., the containment problem between ordinary and symbolic powers of ideals, in the theory of…
We afford the problem of counting the blocks of a given length made with symbols drawn from an alphabet and relate this number to Fibonacci-like recurrent relations. The recurrence polynomia allows to calculate the limit ratio of two…
This chapter presents some of the links between automata theory and symbolic dynamics. The emphasis is on two particular points. The first one is the interplay between some particular classes of automata, such as local automata and results…
Recently, chains of increasing symmetric ideals have attracted considerable attention. In this note, we summarize some results and open problems concerning the asymptotic behavior of several algebraic and homological invariants along such…
We provide a survey of results from symbolic dynamics and algebraic topology relating to Grout, a new user-friendly program developed to calculate combinatorial properties and topological invariants of a large class of symbolic…
We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…
We survey old and new approaches to the study of symbolic powers of ideals. Our focus is on the symbolic Rees algebra of an ideal, viewed both as a tool to investigate its symbolic powers and as a source of challenging problems in its own…
Some proofs of the problems of the basic statistics proposed for numeric symbolic data.
We compute the regularity of powers and symbolic powers of edge ideals of all cubic circulant graphs. In particular, we establish Conjecture of Minh for cubic circulant graphs.
In this paper, we investigate containment statements between symbolic and ordinary powers and bounds on the Waldschmidt constant of defining ideals of points in projective spaces. We establish the stable Harbourne conjecture for the…
Symbolic regression is a type of discrete optimization problem that involves searching expressions that fit given data points. In many cases, other mathematical constraints about the unknown expression not only provide more information…
Symbolic summation as an active research topic of symbolic computation provides efficient algorithmic tools for evaluating and simplifying different types of sums arising from mathematics, computer science, physics and other areas. Most of…
This note addresses the continuum problem, taking advantage of the breakthrough mentioned in the subtitle, and relating it to many recent advances occurring in set theory.
We consider an intersection of past and future property of multivariate stationary processes which is the key to deriving various representation theorems for their linear predictor coefficient matrices. We extend useful spectral…
We present here a note which synthesizes our previous ideas concerning some problems in cosmology, and the numerical correspondences between the physical constants that we could deduce.
We discuss the property of (almost) complete intersection of LSS-ideals of graphs of some special forms, like trees, unicyclic, and bicyclic graphs. Further, we give a sufficient condition for the complete intersection property of twisted…
In this short note, we simply collect some known results about representing algebraic cycles by various kind of "nice" (e.g. smooth, local complete intersection, products of local complete intersection) algebraic cycles, up to rational…
In this paper we investigate cumulative hierarchies of functions on structures, or cumulative powers, and study their properties. Particularly, we show how they extend the preservation phenomena of reduced powers, direct powers and…
These notes are an introduction to some basic aspects of the Castelnuovo-Mumford regularity and related topics such as weak regularity, a*-invariant and partial regularities.