Related papers: Humps for Dyck and for Motzkin paths
We report our experiences with the generalized integration-by-parts algorithm [hep-ph/9609429] in the context of calculations of a realistic one-loop subset of diagrams.
We compute the number of circuits and of loops with multiple crossings in random regular graphs. We discuss the importance of this issue for the validity of the cavity approach. On the one side we obtain analytic results for the infinite…
We describe algorithms for computing the intersection numbers of divisors and of Chern classes of the Hodge bundle on the moduli spaces of stable pointed curves. We also discuss the implementations and the results obtained. There are…
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for…
The cyclicity problem, crucial in analyzing planar vector fields, consists in estimating the number of limit cycles emanating from monodromic singularities. Traditionally, this estimation relies on Lyapunov coefficients. However, in…
The exact path length problem is to determine if there is a path of a given fixed cost between two vertices. This paper focuses on the exact path problem for costs $-1,0$ or $+1$ between all pairs of vertices in an edge-weighted digraph.…
We give some formulas of the James-Hopf maps by using combinatorial methods. An application is to give a product decomposition of the spaces $\Omega\Sigma^2(X)$.
Hopping transport in a one-dimensional system is studied numerically. A fast algorithm is devised to find the lowest-resistance path at arbitrary electric field. Probability distribution functions of individual resistances on the path and…
We introduce and characterize central probability distributions on Littelmann paths. Next we establish a law of large numbers and a central limit theorem for the generalized Pitmann transform. We then study harmonic functions on…
We consider the problem of enumerating Dyck paths staying weakly above the x-axis with a limit to the number of consecutive up steps, or a limit to the number of consecutive down steps. We use Finite Operator Calculus to obtain formulas for…
We evaluate the configuration exponents of various ensembles of Hamiltonian paths drawn on random planar bicubic maps. These exponents are estimated from the extrapolations of exact enumeration results for finite sizes and compared with…
In the study of stratified spaces it is useful to examine spaces of popaths (paths which travel from lower strata to higher strata) and holinks (those spaces of popaths which immediately leave a lower stratum for their final stratum…
We study the path behavior of the simple symmetric walk on some comb-type subsets of Z^2 which are obtained from Z^2 by removing all horizontal edges belonging to certain sets of values on the y-axis. We obtain some strong approximation…
We explore a generating function trick which allows us to keep track of infinitely many statistics using finitely many variables, by recording their individual distributions rather than their joint distributions. Building on previous work…
Polynomial systems occur in many areas of science and engineering. Unlike general nonlinear systems, the algebraic structure enables to compute all solutions of a polynomial system. We describe our massive parallel predictor-corrector…
We consider zigzags in thin complexes. The main result states that the sum of the lengths of all zigzags in an $n$-complexe is equal to the sum of the lengths of all zigzags in all $(n-1)$-faces of this complex, and this sum also is the…
We define a statistic called the weight of oscillating tableaux. Oscillating tableaux, a generalization of standard Young tableaux, are certain walks in Young's lattice of partitions. The weight of an oscillating tableau is the sum of the…
We solve a recent question of Caro, Patk\'os and Tuza by determining the exact maximum number of edges in a bipartite connected graph as a function of the longest path it contains as a subgraph and of the number of vertices in each side of…
We give piecewise affine maps on the unit cube whose symbolic representation is the Dyck shift. This leads to a different way of verifying the chaotic nature of this system, including the computation of entropy.
We study two variations of Nim and Chomp which we call Monotonic Nim and Diet Chomp. In Monotonic Nim the moves are the same as in Nim, but the positions are non-decreasing numbers as in Chomp. Diet-Chomp is a variation of Chomp, where the…