相关论文: Reconstructing a generalized quadrangle with a hem…
We present the tables of feasible parameters of primitive $3$-class $Q$-polynomial association schemes and $4$- and $5$-class $Q$-bipartite association schemes (on up to $2800$, $10000$, and $50000$ vertices, respectively), accompanied by a…
This work explores new arithmetic and combinatorial structures arising from the interplay between Farey-type graphs, Fibonacci expansions, and operadic constructions. We introduce Fibonadic numbers, defined as an inverse limit under the…
We provide several new $q$-congruences for truncated basic hypergeometric series, mostly of arbitrary order. Our results include congruences modulo the square or the cube of a cyclotomic polynomial, and in some instances, parametric…
The group $PGL(2,q)$ has an embedding into $PGL(3,q)$ such that it acts as the group fixing a nonsingular conic in $PG(2,q)$. This action affords a coherent configuration $R(q)$ on the set $L(q)$ of non-tangent lines of the conic. We show…
We study some classical integrable systems naturally associated with multiplicative quiver varieties for the (extended) cyclic quiver with $m$ vertices. The phase space of our integrable systems is obtained by quasi-Hamiltonian reduction…
This paper deals with numerical methods for reconstruction of inhomogeneous conductivities. We use the concept of Generalized Polarization Tensors, which were introduced in [3], to do reconstruction. Basic resolution and stability analysis…
Applying results from partial difference sets, quadratic forms, and recent results of Brouwer and Van Dam, we construct the first known amorphic association scheme with negative Latin square type graphs and whose underlying set is a…
This paper deals with the notion of quadratic differential in spherical CR geometry (or more generally on strictly pseudoconvex CR manifolds). We get to this notion by studying a splitting of Rumin complex and discuss its first features…
A jet algorithm must specify how to (re-)combine different partons or towers into a single four-vector. Various recombination schemes have been used experimentally to examine the transverse energy profile of jets in hadron colliders.…
This is preprint HAL-00429963 (2009). I describe a combinatorial construction of the cohomology classes in compactified moduli spaces of curves $\widehat{Z}_{I}\in H^{*}(\bar{\mathcal{M}}_{g,n})$ starting from the following data: an odd…
\noindent We propose a set of rules for constructing composite leptons and quarks as triply occupied quasiparticles, in the quaternionic quantum mechanics of a pair of Harari-Shupe preons $T$ and $V$. The composites fall into two classes,…
The_commuting variety_ is the pairs of NxN matrices (X,Y) such that XY = YX. We introduce the_diagonal commutator scheme_, {(X,Y) : XY-YX is diagonal}, which we prove to be a reduced complete intersection, one component of which is the…
A connected graph is 4-connected if it contains at least five vertices and removing any three of them does not disconnect it. A frequent preprocessing step in graph drawing is to decompose a plane graph into its 4-connected components and…
In this thesis, the connection between recently introduced algebraic structures (tridiagonal algebra, $q$-Onsager algebra, generalized $q-$Onsager algebras), related representation theory (tridiagonal pair, Leonard pair, orthogonal…
A known Kronecker construction of completely regular codes has been investigated taking different alphabets in the component codes. This approach is also connected with lifting constructions of completely regular codes. We obtain several…
For any integer $\rho \geq 1$ and for any prime power q, the explicit construction of a infinite family of completely regular (and completely transitive) q-ary codes with d=3 and with covering radius $\rho$ is given. The intersection array…
We show that the Catalan-Schroeder convolution recurrences and their higher order generalizations can be solved using Riordan arrays and the Catalan numbers. We investigate the Hankel transforms of many of the recurrence solutions, and…
Association schemes were originally introduced by Bose and his co-workers in the design of statistical experiments. Since that point of inception, the concept has proved useful in the study of group actions, in algebraic graph theory, in…
We show the relationship between the mathematical framework used in recent papers by H.C. Rosu, S.C. Mancas and P. Chen (2014) and the second-order confluent supersymmetric quantum mechanics. In addition, we point out several immediate…
A $pseudo$-$oval$ of a finite projective space over a finite field of odd order $q$ is a configuration of equidimensional subspaces that is essentially equivalent to a translation generalised quadrangle of order $(q^n,q^n)$ and a Laguerre…