Related papers: Log-balanced combinatorial sequences
We recall the definition and the properties of a moment sequence and recall that all real sequences that have a finite rank of its Hankel matrix (see definition in the sequel) satisfy a homogeneous linear equation with constant…
A special case of the satisfiability problem, in which the clauses have a hierarchical structure, is shown to be solvable in linear time, assuming that the clauses have been represented in a convenient way.
We present sufficient conditions for total positivity of Riordan arrays. As applications we show that many well-known combinatorial triangles are totally positive and many famous combinatorial numbers are log-convex in a unified approach.
We show that the likelihood function for a multinomial vector observed under arbitrary interval censoring constraints on the frequencies or their partial sums is completely log-concave by proving that the constrained sample spaces comprise…
A set of words, also called a language, is letter-balanced if the number of occurrences of each letter only depends on the length of the word, up to a constant. Similarly, a language is factor-balanced if the difference of the number of…
In this paper, we consider integral linear constraints and the dissipation inequality with linear supply rates for certain sets of trajectories confined pointwise in time to a convex cone which belongs to a finite-dimensional normed vector…
The fundamental question considered in algorithms on strings is that of indexing, that is, preprocessing a given string for specific queries. By now we have a number of efficient solutions for this problem when the queries ask for an exact…
We give equivalent conditions for a monomial sequence to be a d-sequence or a proper sequence, and a sufficient condition for a monomial sequence to be an s-sequence in order to compute invariants of the symmetric algebra of the ideal…
A classical result of Kahn and Saks states that given any partially ordered set with two distinguished elements, the number of linear extensions in which the ranks of the distinguished elements differ by $k$ is log-concave as a function of…
A general sufficient condition for the convergence of subsequences of solutions of non-autonomous, nonlinear difference equations and systems is obtained. For higher order equations the delay sizes and patterns play essential roles in…
We construct and analyze a family of coherent states built on sequences of integers originating from the solution of the boson normal ordering problem. These sequences generalize the conventional combinatorial Bell numbers and are shown to…
It is shown that (1) if a good set has finitely many related components, then they are full, (2) loops correspond one-to-one to extreme points of a convex set. Some other properties of good sets are discussed.
For an arbitrary homogeneous linear recurrence sequence of order d with constant coefficients, we derive recurrence relations for all subsequences with indices in arithmetic progression. The coefficients of these recurrences are given…
We prove a lemma, which we call the Order Ideal Lemma, that can be used to demonstrate a wide array of log-concavity and log-convexity results in a combinatorial manner using order ideals in distributive lattices. We use the Order Ideal…
We develop a theory of combinatorial games that is appropriate for describing positions in Hex and other monotone set coloring games. We consider two natural conditions on such games: a game is monotone if all moves available to both…
Many complex systems share two characteristics: 1) they are stochastic in nature, and 2) they are characterized by a large number of factors. At the same time, various natural complex systems appear to have two types of intertwined…
For a prime $p\ge 5$ let $q_0,q_1,\ldots,q_{(p-3)/2}$ be the quadratic residues modulo $p$ in increasing order. We study two $(p-3)/2$-periodic binary sequences $(d_n)$ and $(t_n)$ defined by $d_n=q_n+q_{n+1}\bmod 2$ and $t_n=1$ if…
Asymmetric combination of logics is a formal process that develops the characteristic features of a specific logic on top of another one. Typical examples include the development of temporal, hybrid, and probabilistic dimensions over a…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
The flow of contracting systems contracts 1-dimensional parallelotopes, i.e., line segments, at an exponential rate. One reason for the usefulness of contracting systems is that many interconnections of contracting sub-systems yield an…