Related papers: Congruence for lattice path models with filter res…
Logarithmic Conformal Field Theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self avoiding walks, etc.), or of critical points in several classes of disordered systems…
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 review the construction of exactly solvable lattice models whose continuum limits are $N=2$ supersymmetric models. Both critical and off-critical models are discussed. The approach we take is to first find lattice models with natural…
We discuss the successes and limitations of statistical sampling for a sequence of models studied in the context of lattice QCD and emphasize the need for new methods to deal with finite-density and real-time evolution. We show that these…
Andrews imposed parity restrictions on the Rogers-Ramanujan-Gordon type partitions, yielding fruitful results. These results were later, advanced by Kur\c{s}ung\"{o}z, Kim, and Yee. In this paper, we construct a bijection between lattice…
In this paper, we study the problem of map matching with travel time constraints. Given a sequence of $k$ spatio-temporal measurements and an embedded path graph with travel time costs, the goal is to snap each measurement to a close-by…
The coincidence problem for planar patterns with $N$-fold symmetry is considered. For the N-fold symmetric module with $N<46$, all isometries of the plane are classified that result in coincidences of finite index. This is done by…
The quantum query complexity of subgraph-containment problems, which ask whether a given subgraph $H$ is present in an input graph $G$, has been the subject of considerable study. However, even for relatively simple subgraphs, such as paths…
Lattice rules and polynomial lattice rules are quadrature rules for approximating integrals over the $s$-dimensional unit cube. Since no explicit constructions of such quadrature methods are known for dimensions $s > 2$, one usually has to…
In this paper, we consider a problem which we call LTL$_f$ model checking on paths: given a DFA $\mathcal{A}$ and a formula $\phi$ in LTL on finite traces, does there exist a word $w$ such that every path starting in a state of…
We present a set of general results on structural features of the $q$-state Potts model partition function $Z(G,q,v)$ for arbitrary $q$ and temperature Boltzmann variable $v$ for various lattice strips of arbitrarily great width $L_y$…
Motzkin paths are simple yet important combinatorial objects. In this paper, we consider families of Motzkin paths with restrictions on peak heights, valley heights, upward-run lengths, downward-run lengths, and flat-run lengths. This paper…
We consider the problem of Data Flow Analysis over monotone data flow frameworks with a finite lattice. The problem of computing the Maximum Fixed Point (MFP) solution is shown to be P-complete even when the lattice has just four elements.…
A foundational question in the theory of linear compartmental models is how to assess whether a model is structurally identifiable -- that is, whether parameter values can be inferred from noiseless data -- directly from the combinatorics…
In this paper, we derive several formulas of counting families of non-intersecting paths for two-sided ladder-shaped regions. As an application, we give a new proof to a combinatorial interpretation of Fibonacci numbers obtained by G.…
We consider the problem of counting lattice points contained in domains in $\mathbb{R}^d$ defined by products of linear forms and we show that the normalized discrepancies in these counting problems satisfy non-degenerate Central Limit…
Given any full rank lattice and a natural number N , we regard the point set given by the scaled lattice intersected with the unit square under the Lambert map to the unit sphere, and show that its spherical cap discrepancy is at most of…
On the basis of the canonical quantization procedure of a system defined on a cubic lattice, we propose a new method, in which resolutions of unity expressed in terms of eigenvectors are naturally provided, to find eigenvectors of field…
The degree of symmetry of a combinatorial object, such as a lattice path, is a measure of how symmetric the object is. It typically ranges from zero, if the object is completely asymmetric, to its size, if it is completely symmetric. We…
The structure of the tensor product representation v_{\lambda_1}(x)\otimes V_{\lambda_2}(y) of U_q(\hat sl_2) is investigated at roots of unity. A polynomial identity is derived as an outcome. Also, new bases of v_{\lambda_1}(x)\otimes…