Related papers: Paths for Z_k parafermionic models
The Z_k parafermionic conformal field theories, despite the relative complexity of their modes algebra, offer the simplest context for the study of the bases of states and their different combinatorial representations. Three bases are…
The states in the irreducible modules of the minimal models can be represented by infinite lattice paths arising from consideration of the corresponding RSOS statistical models. For the M(p,2p+1) models, a completely different path…
This is the second of two articles (independent of each other) devoted to the analysis of the path description of the states in su(2)_k WZW models. Here we present a constructive derivation of the fermionic character at level k based on…
We introduce a new representation of the paths of the Forrester-Baxter RSOS models which represents the states of the irreducible modules of the minimal models M(p',p). This representation is obtained by transforming the RSOS paths, for the…
This is the first of two articles devoted to the analysis of the path description of the states in su(2)_k WZW models, a representation well suited for constructive derivations of the fermionic characters. In this first article, the cases…
We present a new path description for the states of the non-unitary M(k+1,2k+3) models. This description differs from the one induced by the Forrester-Baxter solution, in terms of configuration sums, of their restricted-solid-on-solid…
Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset $\osp(1,2)_k/\uh(1)$. The first one is formulated in terms of the two fundamental (i.e., lowest dimensional)…
We study the combinatorics of the change of basis of three representations of the stationary state algebra of the two parameter simple asymmetric exclusion process. Each of the representations considered correspond to a different set of…
We present three bijections, the first between little Schr\"{o}der paths and a class of growth-constrained integer sequences, the second between lattice paths consisting of steps with nonnegative slope and another class of…
We consider sl(2) minimal conformal field theories on a cylinder from a lattice perspective. To each allowed one-dimensional configuration path of the A_L Restricted Solid-on-Solid (RSOS) models we associate a physical state |h> and a…
We describe a bijection between $(k,k)$-Fuss-Schr\"oder paths of type $\lambda$ and certain rooted plane forests with $n(k+1)+2$ vertices. This yields a recursion which allows us to analytically enumerate the number of large…
Lattice paths are important tools on solving some combinatorial identities. This note gives a new bijection between unbalanced Dyck path (a path that never reaches the diagonal of the lattice) and NE (North and East only) lattice path from…
We study semi-infinite paths of the radial spanning tree (RST) of a Poisson point process in the plane. We first show that the expectation of the number of intersection points between semi-infinite paths and the sphere with radius $r$ grows…
The purpose of the paper is to suggest a new method which allows one to study multiple coherent reflection/transmissions by partially transparent interfaces (e.g. in multi-layer mesoscopic structures or grain boundaries in high-Tc's) in the…
We derive a path counting formula for two-dimensional lattice path model with filter restrictions in the presence of long steps, source and target points of which are situated near the filters. This solves a problem of finding an explicit…
Simple bosonic path integral representation for path ordered exponent is derived. This representation is used, at first, to obtain new variant of non-Abelian Stokes theorem. Then new pure bosonic worldline path integral representations for…
We first briefly review the role of lattice paths in the derivation of fermionic expressions for the M(p,p') minimal model characters of the Virasoro Lie algebra. We then focus on the recently introduced half-lattice paths for the…
Kim and Drake used generating functions to prove that the number of 2-distant noncrossing matchings, which are in bijection with little Schroeder paths, is the same as the weight of Dyck paths in which downsteps from even height have weight…
A bijection is presented between (1): partitions with conditions $f_j+f_{j+1}\leq k-1$ and $ f_1\leq i-1$, where $f_j$ is the frequency of the part $j$ in the partition, and (2): sets of $k-1$ ordered partitions $(n^{(1)}, n^{(2)}, ...,…
We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the $d$-dimensional…