相关论文: A reflection principle for nonintersecting paths a…
In a recent preprint, Lai worked out the quotient of generating functions of weighted lozenge tilings of two "half hexagons with lateral dents" which differ only in width. Lai achieved this by using "graphical condensation" (i.e.,…
In this paper, we mainly consider a combinatoric explanation for block Pfaffians in terms of non-intersecting paths, as a generalization of results obtained by Stembridge. As applications, we demonstrate how are generating functions of…
We deal with unweighted and weighted enumerations of lozenge tilings of a hexagon with side lengths $a,b+m,c,a+m,b,c+m$, where an equilateral triangle of side length $m$ has been removed from the center. We give closed formulas for the…
MacMahon enumerated the plane partitions in an $a \times b \times c$ box. These are in bijection to lozenge tilings of a hexagon, to certain perfect matchings, and to families of non-intersecting lattice paths. In this work we consider more…
Koutschan, Krattenthaler and Schlosser recently considered a family of binomial determinants. In this work, we give combinatorial interpretations of two subclasses of these determinants in terms of domino tilings and nonintersecting lattice…
In a recent preprint, Lai showed that the quotient of generating functions of weighted lozenge tilings of two "half hexagons with lateral dents", which differ only in width, factors nicely, and the same is true for the quotient of…
This article addresses the problem of enumerating the tilings of a plane by lozenges, under the restriction that these tilings be doubly periodic. Kasteleyn's Pfaffian method is applied to compute the generating function of those…
The combinatorics of certain osculating lattice paths is studied, and a relationship with oscillating tableaux is obtained. More specifically, the paths being considered have fixed start and end points on respectively the lower and right…
In this paper we present an algorithm for enumerating without repetitions all the non-crossing generically minimally rigid bar-and-joint frameworks under edge constraints (also called constrained non-crossing Laman frameworks) on a given…
We prove a product formula for the remaining cases of the weighted enumeration of self-complementary plane partitions contained in a given box where adding one half of an orbit of cubes and removing the other half of the orbit changes the…
It is well known that there are close connections between non-intersecting processes in one dimension and random matrices, based on the reflection principle. There is a generalisation of the reflection principle for more general (e.g.…
In these proceedings we will review recent progress in applying ideas from the mathematical framework of twisted cohomology to the study of canonical differential equations for Feynman integrals. Firstly, we will show how the intersection…
Nonexpansive mappings play a central role in modern optimization and monotone operator theory because their fixed points can describe solutions to optimization or critical point problems. It is known that when the mappings are sufficiently…
We enumerate lattice paths in the planar integer lattice consisting of positively directed unit vertical and horizontal steps with respect to a specific elliptic weight function. The elliptic generating function of paths from a given…
We study a family of substitution tilings with similar right triangles of two sizes which is obtained using the substitution rule introduced in [Danzer, L. and van Ophuysen, G. A species of planar triangular tilings with inflation factor…
Intersection distribution and non-hitting index are concepts introduced recently by Li and Pott as a new way to view the behaviour of a collection of finite field polynomials. With both an algebraic interpretation via the intersection of a…
In a recent preprint, Lai and Rohatgi compute the generating functions of lozenge tilings of "quartered hexagons with dents" by applying the method of "graphical condensation". The purpose of this note is to exhibit how (a generalization…
After recalling the definition of Grassmann algebra and elements of Grassmann--Berezin calculus, we use the expression of Pfaffians as Grassmann integrals to generalize a series of formulas relating generating functions of paths in digraphs…
We find the Martin boundary for the Young-Fibonacci lattice YF. Along with the lattice of Young diagrams, this is the most interesting example of a differential poset. The Martin boundary construction provides an explicit Poisson-type…
We identify a structural pattern in the construction of known infinite families of trees whose independence polynomials are not log-concave. Using this pattern and properties of polynomial ring ideals, we derive linear recurrences for these…