A labeled set partition is a partition of a set of integers whose arcs are labeled by nonzero elements of an abelian group A. Inspired by the action of the linear characters of the unitriangular group on its supercharacters, we define a group action of An on the set of A-labeled partitions of an (n + 1)-set. By investigating the orbit decomposition of various families of set partitions under th...

We study a natural random walk over the upper triangular matrices, with entries in the field Z2, generated by steps which add row i + 1 to row i. We show that the mixing time of the lazy random walk is O(n) which is optimal up to constants. Our proof makes key use of the linear structure of the group and extends to walks on the upper triangular matrices over the fields Zq for q prime.

In this paper, we study the simple eigenvectors of two hypomorphic matrices using linear algebra. We also give new proofs of results of Godsil and McKay.

We study the realizability over R of representations of the group U(n) of upper-triangular n× n matrices over F2. We prove that all the representations of U(n) are realizable over R if n ≤ 12, but that if n ≥ 13, U(n) has representations not realizable over R. This theorem is a variation on a result that can be obtained by combining work of J. Arregi and A. Vera-López and of the authors, but th...

this paper introduces a numerical method for solving the vasicek model by using a stochastic operational matrix based on the triangular functions (tfs) in combination with the collocation method. the method is stated by using conversion the vasicek model to a stochastic nonlinear system of $2m+2$ equations and $2m+2$ unknowns. finally, the error analysis and some numerical examples are provided...

for the analysis of structures, the first step consists of configuration processing followed by data generation. this step is the most time consuming part of the analysis for large-scale structures. in this paper new graph products called triangular and circular graph products are developed for the formation of the space structures. the graph products are extensively used in graph theory and co...

‎let $mathcal a$ and $mathcal b$ be unital rings‎, ‎and $mathcal m$‎ ‎be an $(mathcal a‎, ‎mathcal b)$-bimodule‎, ‎which is faithful as a‎ ‎left $mathcal a$-module and also as a right $mathcal b$-module‎. ‎let ${mathcal u}=mbox{rm tri}(mathcal a‎, ‎mathcal m‎, ‎mathcal‎ ‎b)$ be the triangular ring and ${mathcal z}({mathcal u})$ its‎ ‎center‎. ‎assume that $f:{mathcal u}rightarrow{mathcal u}$ is...

Triangular B-splines are a new tool for modeling a broad class of objects de ned over arbitrary, non-rectangular domains. They provide an elegant and uni ed representation scheme for all piecewise continuous polynomial surfaces over planar triangulations. To enhance the power of this model, we propose triangular NURBS, the rational generalization of triangular B-splines, with weights as additio...

We introduce a Hom-type generalization of quantum groups, called quasi-triangular Hom-bialgebras. They are non-associative and non-coassociative analogues of Drinfel’d’s quasitriangular bialgebras, in which the non-(co)associativity is controlled by a twisting map. A family of quasi-triangular Hom-bialgebras can be constructed from any quasi-triangular bialgebra, such as Drinfel’d’s quantum env...

The triangular fibrocartilage complex (TFCC) is an anatomically and biomechanically important structure. Repair of radial-sided TFCC tear has previously been challenging. We designed a new method of radial-sided TFCC tear repair and found that it was also applicable for ulnar-sided TFCC tear repair. From October 2006 to December 2010, 10 patients underwent this operation and were reviewed: 9 me...