Related papers: The relative lattice path operad

Twisted vertex operators based on rational lattices have had many applications in vertex operator algebra theory and conformal field theory. In this paper, ``relativized'' twisted vertex operators are constructed in a general context based…

We introduce a canonical operator-theoretic construction associated to a finite geometric lattice, in which a simple nonassociative ``diamond product'' on the lattice basis gives rise to a family of creation operators indexed by atoms and a…

We propose a new formulation of lattice theory. It is given by a matrix form and suitable for satisfying Leibniz rule on lattice. The theory may be interpreted as a multi-flavor system. By realizing the difference operator as a commutator,…

Combinatorial objects such as rooted trees that carry a recursive structure have found important applications recently in both mathematics and physics. We put such structures in an algebraic framework of operated semigroups. This framework…

We prove the statement in the title, solving in this way a conjecture stated by Ginot for manifolds with corners. Along the way, we establish a derived Swiss-cheese additivity theorem and an alternative proof for the hyperdescent of…

Lattice paths called $\ell$-Schr\"oder paths are introduced. They are paths on the upper half-plane consisting of $\ell+2$ types of steps: $(i,\ell-i)$ for $i=0,\ldots,\ell$, and $(1,-1)$. Those paths generalize Schr\"oder paths and some…

We consider lattice field theories with topological actions, which are invariant against small deformations of the fields. Some of these actions have infinite barriers separating different topological sectors. Topological actions do not…

We review several well-known operads of compactified configuration spaces and construct several new such operads, C, in the category of smooth manifolds with corners whose complexes of fundamental chains give us (i) the 2-coloured operad of…

We introduce two topological non-$\Sigma$ operad structures on planar line arrangements subject to a certain geometric order condition, ensuring a well-defined notion of particle ordering on a distinguished line. This is interpreted in…

We develop the structure theory for transformations of weakly geometric rough paths of bounded $1 < p$-variation and their controlled paths. Our approach differs from existing approaches as it does not rely on smooth approximations. We…

It is well known that the forgetful functor from symmetric operads to nonsymmetric operads has a left adjoint $Sym_1$ given by product with the symmetric group operad. It is also well known that this functor does not affect the category of…

This paper shows that the semi-direct product construction for $G$-operads and the levelwise Borel construction for $G$-cooperads are intertwined by the topological operadic bar construction. En route we give a generalization of the bar…

We propose a class of pure states of two-dimensional lattice systems realizing topological order associated with unitary rational vertex operator algebras. We show that the states are well-defined in the thermodynamic limit and have…

We use lattice topology as a laboratory to compare the Wilson action (WA) with the Symanzik-Weisz (SW) action constructed from a combination of (1x1) and (1x2) Wilson loops, and the estimate of the renormalization trajectory (RT) from a…

Consider an Archimedean partially ordered vector space $X$ with generating cone (or, more generally, a pre-Riesz space $X$). Let $P$ be a linear projection on $X$ such that both $P$ and its complementary projection $I - P$ are positive; we…

We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the Packed Swiss Cheese Cosmology models. As the action functional for gravity we consider the…

For Paley-Wiener functions on weighted combinatorial finite or infinite graphs we develop a weighted sampling theory in which samples are defined as inner products with weight functions (measuring devices). Three reconstruction methods are…

We study the properties of shifted vertex operator algebras, which are vertex algebras derived from a given theory by shifting the conformal vector. In this way, we are able to exhibit large numbers of vertex operator algebras which are…

We conjecture a combinatorial formula for the monomial expansion of the image of any Schur function under the Bergeron-Garsia nabla operator. The formula involves nested labeled Dyck paths weighted by area and a suitable "diagonal…

We consider weighted graphs, we equip them with a metric structure given by a weighted distance, and we discuss essential self-adjointness for weighted graph Laplacians and Schr\"odinger operators in the metrically non complete case.