Related papers: Oriented Steiner Triple Systems, Steiner Products,…
Niebrzydowski tribrackets are ternary operations on sets satisfying conditions obtained from the oriented Reidemeister moves such that the set of tribracket colorings of an oriented knot or link diagram is an invariant of oriented knots and…
We study the AKNS($N$) hierarchy for $N=3,4,5,6$. We give the Hirota bilinear forms of these systems and present local and nonlocal reductions of them. We give the Hirota bilinear forms of the reduced equations. The compatibility of the…
Family algebraic structures indexed by a semigroup first appeared in the algebraic aspects of renormalizations in quantum field theory. The concept of the Rota-Baxter family and its relation with (tri)dendriform family algebras have been…
The aim of this paper is to numerically investigate the orbital dynamics of the circular planar restricted problem of five bodies. By numerically integrating several large sets of initial conditions of orbits we classify them into three…
This paper answers a fundamental question in the theory of Steiner operations (StOps) as defined and studied in the monograph, "Global Methods for Combinatorial Isoperimetric Problems" (GMCIP). StOps are morphisms for combinatorial…
Association Schemes and coherent configurations (and the related Bose-Mesner algebra and coherent algebras) are well known in combinatorics with many applications. In the 1990s, Mesner and Bhattacharya introduced a three-dimensional…
In vivo and in vitro systems of cells and extra-cellular matrix (ECM) systems are well known to form ordered patterns of orientationally aligned fibers. Here, we interpret them as active analogs of the (disordered) isotropic to the…
This paper provides a dendriform-tree setting for Fliess operators with matrix-valued inputs. This class of analytic nonlinear input-output systems is convenient, for example, in quantum control. In particular, a description of such Fliess…
We construct growth bijections for bipolar oriented planar maps and for Schnyder woods. These give direct combinatorial proofs of several counting identities for these objects. Our method mainly uses two ingredients. First, a slit-slide-sew…
The classification, up to isomorphism, of all self-embedding monomial power permutations of Hamming Steiner triple systems of order n=2^m-1 for small m, m < 23, is given. As far as we know, for m in {5,7,11,13,17,19}, all given…
A noncommutative Jordan algebra of a specific type is attached to any (-1,-1)-balanced Freudenthal Kantor triple system, in such a way that the triple product in this system is determined by the binary product in the algebra. Over fields of…
It is well known that every compact oriented 3-manifold admits an ideal triangulation, and that any two such triangulations with at least two ideal tetrahedra are related by a sequence of Pachner $2$-$3$ moves. Motivated by constructions in…
Let $D=(V(D), A(D))$ be a digraph of order $n$ and let $S\subseteq V(D)$ with $2\leq |S|\leq n$. A directed cycle $C$ of $D$ is called a directed $S$-Steiner cycle (or, an $S$-cycle for short) if $S\subseteq V(C)$. Steiner cycles have…
An oriented graph is a directed graph which can be obtained from a simple undirected graph by orienting its edges. In this paper we show that any oriented graph G on n vertices with minimum indegree and outdegree at least (1/2-o(1))n…
Let (A,H,D) be a spectral triple, namely: A is a C*-algebra, H is a Hilbert space on which A acts and D is a selfadjoint operator with compact resolvent such that the set of elements of A having a bounded commutator with D is dense. A…
We note that a strongly minimal Steiner $k$-Steiner system $(M,R)$ from (Baldwin-Paolini 2020) can be `coordinatized' in the sense of (Gantner-Werner 1975) by a quasigroup if $k$ is a prime-power. But for the basic construction this…
A ferrimagnetic spin model composed of $S=1/2$ spin-dimers and $S=5/2$ spin-chains is studied by combining the bond-operator representation (for $S=1/2$ spin-dimers) and Holstein-Primakoff transformation (for $S=5/2$ spins). A finite…
In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the…
We introduce an order parameter for symmetry-protected phases in one dimension which allows to directly identify those phases. The order parameter consists of string-like operators and swaps, but differs from conventional string order…
Let $P_n$ denote the $n$-th linear ordering polytope. We define projections from $P_n$ to the $n$-th permutahedron and to the $(n-1)$-st linear ordering polytope. Both projections are equivariant with respect to the natural $\Sn$-action and…