Related papers: Lattice paths and quiver generating series with hi…
Let $C$ be a simply laced generalized Cartan matrix. Given an element $b$ of the generalized braid semigroup related to $C$, we construct a collection of mutation-equivalent quivers with potentials. A quiver with potential in such a…
In the first part of this paper I give an elementary overview about some number sequences which count various sorts of lattice paths in strips along the x-axis and compute their generating functions in terms of Fibonacci and Lucas…
The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…
We introduce a presentation of the Chow ring of a matroid by a new set of generators, called "simplicial generators." These generators are analogous to nef divisors on projective toric varieties, and admit a combinatorial interpretation via…
We derive a series of results on random walks on a d-dimensional hypercubic lattice (lattice paths). We introduce the notions of terse and simple paths corresponding to the path having no backtracking parts (spikes). These paths label…
The combinatorics of the BPHZ subtraction scheme for a class of ladder graphs for the three point vertex in $\phi^3$ theory is transcribed into certain connectivity relations for marked chord diagrams (knots with transversal intersections).…
Recent advances in Quantum Topology assign $q$-series to knots in at least three different ways. The $q$-series are given by generalized Nahm sums (i.e., special $q$-hypergeometric sums) and have unknown modular and asymptotic properties.…
The quiver Yangians were originally defined for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds, and serve as BPS algebras of these systems. Their characters reproduce the unrefined BPS indices, which…
We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions,…
The number of Borel orbits in polarizations (the symmetric variety $SL(n)/S(GL(p)\times GL(q))$) is analyzed, various (bivariate) generating functions are found. Relations to lattice path combinatorics are explored.
It is described the group of arrowy permutations (that is extension of symmetric group) and the consequent process of generation of GL(n) and some its subgroups by this combinatoric group and its subgroups.
We explore more the properties of bipartite knots and its rich combinatorial structure.
At moderate and large momentum transfer, high energy vector meson photoproduction and Compton scattering can be consistently explained by mechanisms based on interactions and exchanges of constituent quarks and gluons. This opens an…
Certain families of combinatorial objects admit recursive descriptions in terms of generating trees: each node of the tree corresponds to an object, and the branch leading to the node encodes the choices made in the construction of the…
We collect statistics which consist of the coefficients in the expansion of the generating polynomials that count the Kauffman states associated with certain classes of pretzel knots having n tangles, of r half-twists respectively.
We describe a block-spin-like transformation on a simplified subset of the space of supersymmetric quiver gauge theories that arise on the worldvolumes of D-brane probes of orbifold geometries, by sequentially Higgsing the gauge symmetry in…
As part of the study of correspondence functors, the present paper investigates their tensor product and proves some of its main properties. In particular, the correspondence functor associated to a finite lattice has the structure of a…
We consider simply generated trees and study multiplicative functions on rooted plane trees. We show that the associated generating functions satisfy differential equations or difference equations. Our approach considers B-series from…
Degeneracy loci polynomials for quiver representations generalize several important polynomials in algebraic combinatorics. In this paper we give a nonconventional generating sequence description of these polynomials, when the quiver is of…
A state generating is introduced to determine the Jones polynomial of a link. Formulae for two infinite families of knots are shown by applying this method, the second family of which are proved to be non-alternating. Moreover, the method…