Related papers: Periodic Parallelogram Polyominoes
We classify recurrent configurations of the sandpile model on the complete bipartite graph K_{m,n} in which one designated vertex is a sink. We present a bijection from these recurrent configurations to decorated parallelogram polyominoes…
We develop several combinatorial notions about laminations, some with clear implications for parameter space. We introduce a simplified class of laminations called finite dynamical laminations (FDL). In order to count FDL, we introduce…
When $p(t)$ is a polynomial of degree $d$, $k$-th column of the Riordan array $\bigl(1/(1 - t^{d+1}), tp(t)\bigr)$ is an eventually periodic sequence with the repeating part beginning at the $1 + (k-1)(d+1)$-st term. The pre-periodic terms…
In this paper we consider a restricted class of convex polyominoes that we call Z-convex polyominoes. Z-convex polyominoes are polyominoes such that any two pairs of cells can be connected by a monotone path making at most two turns (like…
A polyomino is a finite, edge-connected set of cells in the plane. At the present time, an enumeration of all polyominoes is nowhere in sight. On the other hand, there are several subsets of polyominoes for which generating functions are…
Ouroboros functions have shown some interesting properties when subjected to conventional operations. The aim of this paper is to continue our investigation and prove some additional properties of these functions. Using algebraic methods,…
The aim of this chapter is to provide an adequate graph theoretic framework for the description of periodic bifurcations which have recently been discovered in descendant trees of finite p-groups. The graph theoretic concepts of rooted…
The Hultman numbers enumerate permutations whose cycle graph has a given number of alternating cycles (they are relevant to the Bafna-Pevzner approach to genome comparison and genome rearrangements). We give two new interpretations of the…
Gluing is a cut and paste construction where the dynamics of a map in a given domain is replaced by a different one, under the condition that the two agree along the gluing curve. Here we consider two polynomials with a finite…
We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match $\langle \Delta_{h_m} e_{n+1},s_{k+1,1^{n-k}}\rangle$, extending in this way the work in (Aval et al.…
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…
We introduce the $k$-bonacci polyominoes, a new family of polyominoes associated with the binary words avoiding $k$ consecutive $1$'s, also called generalized $k$-bonacci words. The polyominoes are very entrancing objects, considered in…
In the present paper we generate binary pseudorandom sequences using generalized polynomials. A generalized polynomial is a function in whose description we not only allow addition and product (as it is the case in usual polynomials) but…
P\'olya trees are rooted, unlabeled trees on $n$ vertices. This paper gives an efficient, new way to generate P\'olya trees. This allows comparing typical unlabeled and labeled tree statistics and comparing asymptotic theorems with…
The matching polynomial of a graph is the generating function of the numbers of its matchings with respect to their cardinality. A graph polynomial is polynomial reconstructible, if its value for a graph can be determined from its values…
Generating random and pseudorandom numbers with a deterministic system is a long-standing challenge in theoretical research and engineering applications. Several pseudorandom number generators based on the inversive congruential method have…
We present and study in this paper a simple algorithm that produces so called growing Parallel Random Apollonian Networks (P-RAN) in any dimension d. Analytical derivations show that these networks still exhibit small-word and scale-free…
Given a finite planar graph, a grove is a spanning forest in which every component tree contains one or more of a specified set of vertices (called nodes) on the outer face. For the uniform measure on groves, we compute the probabilities of…
Finding schedules for pairwise meetings between the members of a complex social group without creating interpersonal conflict is challenging, especially when different relationships have different needs. We formally define and study the…
We introduce area, bounce and dinv statistics on decorated parallelogram polyominoes, and prove that some of their q,t-enumerators match $\langle \Delta_{h_m} e_{n+1}, s_{k+1,1^{n-k}} \rangle$, extending in this way the work in (Aval et al.…