Related papers: Chain lengths in the type $B$ Tamari lattice
In the study of ribbon knots, Lamm introduced symmetric unions inspired by earlier work of Kinoshita and Terasaka. We show an identity between the twisted Alexander polynomials of a symmetric union and its partial knot. As a corollary, we…
A model of two interacting polymer chains has been proposed to study the effect of penetration of one chain in to the other. We show that small chain penetrates more in comparison to the long chain. We also find a condition in which both…
The versatile technology of cold atoms confined in optical lattices allows the creation of a vast number of lattice geometries and interactions, providing a promising platform for emulating various lattice models. This opens the possibility…
This paper focuses on semilattices with adjunctions (SLatas), which are semilattices with a greatest element enriched with a pair of adjoint maps. We develop a spectral-style duality for SLatas, building on prior topological dualities for…
Let L be a join-distributive lattice with length n and width(Ji L) \leq k. There are two ways to describe L by k-1 permutations acting on an n-element set: a combinatorial way given by P.H. Edelman and R.E. Jamison in 1985 and a recent…
We introduce cubic coordinates, which are integer words encoding intervals in the Tamari lattices. Cubic coordinates are in bijection with interval-posets, themselves known to be in bijection with Tamari intervals. We show that in each…
Given a thin strip of paper, tie a knot, connect the ends, and flatten into the plane. This is a physical model of a folded ribbon knot in the plane, first introduced by Louis Kauffman. We study the folded ribbonlength of these folded…
In this paper we define a family of systems which have similarities with the Toda lattice. We construct two Lax pair representations and the associate Poisson structures for these systems. These systems lie between the classical Toda…
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a…
The Ehrhart polynomial of a lattice polygon P is completely determined by the pair (b(P),i(P)) where b(P) equals the number of lattice points on the boundary and i(P) equals the number of interior lattice points. All possible pairs…
We show that Kramers rate theory gives a straightforward, accurate estimate of the closing time $\tau_c$ of a semiflexible polymer that is valid in cases of physical interest. The calculation also reveals how the time scales of chain…
A method is proposed for latticizing a class of supersymmetric gauge theories, including N=4 super Yang-Mills. The technique is inspired by recent work on ``deconstruction''. Part of the target theory's supersymmetry is realized exactly on…
We generalize the Borici-Creutz action in such a way that the position of the second zero and the direction which breaks the hypercubic symmetry can be arbitrarily chosen, and the action has still the correct continuum limit. Minimal…
We prove Thompson's group $F$ has quadratic conjugator length function. That is, for any two conjugate elements of $F$ of length $n$ or less, there exists an element of $F$ of length $O(n^2)$ that conjugates one to the other. Moreover,…
A detailed combinatorial analysis of planar lattice convex polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained. The…
We study heaps of pieces for lattice paths, which give a combinatorial visualization of lattice paths. We introduce two types of heaps: type $I$ and type $II$. A heap of type $I$ is characterized by peaks of a lattice path. We have a…
We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals…
The B\"acklund transformations for the relativistic lattices of the Toda type and their discrete analogues can be obtained as the composition of two duality transformations. The condition of invariance under this composition allows to…
An integral lattice which is generated by some vectors of norm $q$ is called $q$-lattice. Classification of 3-lattices of dimension at most four is given by Mimura (On 3-lattice, 2006). As a expansion, we give a classification of 3-lattices…
Empirical constructions having maximal contact numbers of unit balls as putative best ones are presented for 20-27 balls.