Related papers: Compositionality of planar perfect matchings
We introduce a generalization of semistandard composition tableaux called permuted composition tableaux. These tableaux are intimately related to permuted basement semistandard augmented fillings studied by Haglund, Mason and Remmel. Our…
A graph $H$ is single-crossing if it can be drawn in the plane with at most one crossing. For any single-crossing graph $H$, we give an $O(n^4)$ time algorithm for counting perfect matchings in graphs excluding $H$ as a minor. The runtime…
Symmetry properties of r-times covariant tensors T can be described by certain linear subspaces W of the group ring K[S_r] of a symmetric group S_r. If for a class of tensors T such a W is known, the elements of the orthogonal subspace…
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
In this paper, we provide polynomial-time algorithms for different extensions of the matching counting problem, namely maximal matchings, path matchings (linear forest) and paths, on graph classes of bounded clique-width. For maximal…
The study of finite projective planes involves planar functions, namely, functions f : F_q --> F_q such that, for each nonzero a in F_q, the function c --> f(c+a) - f(c) is a bijection on F_q. Planar functions are also used in the…
We modularly build increasingly larger fragments of the ZX-calculus by modularly adding new generators and relations, at each point, giving some concrete semantics in terms of some category of spans. This is performed using Lack's technique…
The Weisfeiler-Leman (WL) algorithm is a combinatorial procedure that computes colorings on graphs, which can often be used to detect their (non-)isomorphism. Particularly the 1- and 2-dimensional versions 1-WL and 2-WL have received much…
In an undirected graph $G=(V,E)$, we say $(A,B)$ is a pair of perfectly matched sets if $A$ and $B$ are disjoint subsets of $V$ and every vertex in $A$ (resp. $B$) has exactly one neighbor in $B$ (resp. $A$). The size of a pair of perfectly…
We present a new certified and complete algorithm to compute arrangements of real planar algebraic curves. Our algorithm provides a geometric-topological analysis of the decomposition of the plane induced by a finite number of algebraic…
Two immersed triangulations in the plane with the same combinatorics are considered as preimage and image of a discrete immersion $F$. We compare the cross-ratios $Q$ and $q$ of corresponding pairs of adjacent triangles in the two…
Explicit formulas are indicated that compute the product $z \cdot w$ of a level-one element $z \in KK^G(A,{\bf C})$ and any element $w \in KK^G({\bf C},B)$ in splitexact algebraic $KK^G$-theory, or $KK^G$-theory for $C^*$-algebras, with…
We prove a complexity classification theorem that classifies all counting constraint satisfaction problems ($\#$CSP) over Boolean variables into exactly three categories: (1) Polynomial-time tractable; (2) $\#$P-hard for general instances,…
Let $\mathfrak{g}$ be a simply laced Lie algebra, $\widehat{\mathfrak{g}}_1$ the corresponding affine Lie algebra at level one, and $\mathcal{W}(\mathfrak{g})$ the corresponding Casimir W-algebra. We consider…
We study flat Friedmann-Robertson-Walker (FRW) models with a perfect fluid matter source and a scalar field non minimally coupled to matter having a double exponential potential. It is shown that the scalar field almost always diverges to…
As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevisky \cite{[4]}, in this paper, we give the test method of positive…
We define a theory of parameterized algebraic complexity classes in analogy to parameterized Boolean counting classes. We define the classes VFPT and VW[t], which mirror the Boolean counting classes #FPT and #W[t], and define appropriate…
We present elementary mappings between classical lattice models and quantum circuits. These mappings provide a general framework to obtain efficiently simulable quantum gate sets from exactly solvable classical models. For example, we…
Martin Klazar computed the total weight of ordered trees under 12 different notions of weight. The last and perhaps most interesting of these weights, w_{12}, led to a recurrence relation and an identity for which he requested combinatorial…
We revisit the class of column competent matrices and study some matrix theoretic properties of this class. The local $w$-uniqueness of the solutions to the linear complementarity problem can be identified by the column competent matrices.…