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We study a new class of polyominoes, called $p$-Fibonacci polyominoes, defined using $p$-Fibonacci words. We enumerate these polyominoes by applying generating functions to capture geometric parameters such as area, semi-perimeter, and the…
P. Gabriel showed that for an unital ring $R$, there exists a bijective correspondence between the set of Gabriel filters of $R$ and the set of Giraud subcategories of $\mathrm{Mod}(R)$ (see \cite[Lemme 1]{Gabriel1} on page 412). In this…
We consider the two permutation statistics which count the distinct pairs obtained from the last two terms of occurrences of patterns t_1...t_{m-2}m(m-1) and t_1...t_{m-2}(m-1)m in a permutation, respectively. By a simple involution in…
We propose a generalized version of the bisection method where the cutting point between the two subintervals is chosen at random following an arbitrary distribution. We compute expected convergence rates with respect to any arbitrary a…
Theoretical background and an implementation of the (p)-group generation algorithm by Newman and O'Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite…
A permutation can be locally classified according to the four local types: peaks, valleys, double rises and double falls. The corresponding classification of binary increasing trees uses four different types of nodes. Flajolet demonstrated…
In this paper, we define and characterize signed interval graphs and bigraphs introducing the concept of negative interval. Also we have shown that these classes of graphs are respectively a generalization of well known classes of interval…
When each vertex is assigned a set, the intersection graph generated by the sets is the graph in which two distinct vertices are joined by an edge if and only if their assigned sets have a nonempty intersection. An interval graph is an…
We construct a new class of symmetric algebras of tame representation type that are also the endomorphism algebras of cluster tilting objects in 2-Calabi-Yau triangulated categories, hence all their non-projective indecomposable modules are…
Let $\Gamma$ be a connected bridgeless metric graph, and fix a point $v$ of $\Gamma$. We define combinatorial iterated integrals on $\Gamma$ along closed paths at $v$, a unipotent generalization of the usual cycle pairing and the…
A half-square of a bipartite graph $B=(X,Y,E_B)$ has one color class of $B$ as vertex set, say $X$; two vertices are adjacent whenever they have a common neighbor in $Y$. If $G=(V,E_G)$ is the half-square of a planar bipartite graph…
We present a bijection between permutation matrices and descending plane partitions without special parts, which respects the quadruple of statistics considered by Behrend, Di Francesco and Zinn--Justin. This bijection involves the…
We consider the dimer problem on a non-bipartite graph $G$, where there are two types of dimers one of which we regard impurities. Results of simulations using Markov chain seem to indicate that impurities are tend to distribute on the…
We unify several seemingly different graph and digraph classes under one umbrella. These classes are all broadly speaking different generalizations of interval graphs, and include, in addition to interval graphs, also adjusted interval…
In this work we introduce and study tree-like tableaux, which are certain fillings of Ferrers diagrams in simple bijection with permutation tableaux and alternative tableaux. We exhibit an elementary insertion procedure on our tableaux…
In The factorization of the Giry monad (arXiv:1707.00488v2) the author considers two $\sigma$-algebras on convex spaces of functions to the unit interval. One of them is generated by the Boolean subobjects and the other is the…
Combinatorial spiders are a model for the invariant space of the tensor product of representations. The basic objects, webs, are certain directed planar graphs with boundary; algebraic operations on representations correspond to…
In this work, we propose a systematic derivation of resonance-based schemes via normal forms. The main idea is to use an arborification map on decorated trees together with a Butcher-Connes-Kreimer type coproduct and lower-dominant parts…
We show that the vertices of every planar graph can be partitioned into two sets, each inducing a so-called triangle-forest, i.e., a graph with no cycles of length more than three. We further discuss extensions to locally planar graphs.…
We unify and extend previous bijections on plane quadrangulations to bipartite and quasibipartite plane maps. Starting from a bipartite plane map with a distinguished edge and two distinguished corners (in the same face or in two different…