Article history: Received 12 September 2015 Accepted 21 December 2015 Available online xxxx Submitted by R. Brualdi MSC: primary 05E15 secondary 15A21

The self-avoiding walk, restricted to a strip, is considered in the context of linguistic combinatorics. AMS class!Jications: 05A15; 05E15; 60J15

In this note we give explicit formulas for the number of distinct fuzzy subgroups of finite p-groups having a cyclic maximal subgroup. MSC (2010): Primary 20N25, 03E72; Secondary 05E15, 20D30, 20D60.

Given a matrix over a skew field fixing the column .1; : : : ; 1/, we give formulas for a row vector fixed by this matrix. The same techniques are applied to give noncommutative extensions of probabilistic properties of codes. Mathematics Subject Classification (2010). 16Z05, 05E15.

There are two distinct approaches to the study of initial value problem of the periodic box-ball systems. One way is the rigged configuration approach due to Kuniba–Takagi–Takenouchi and another way is the 10-elimination approach due to Mada–Idzumi–Tokihiro. In this paper, we describe precisely interrelations between these two approaches. Mathematics Subject Classification (2000) 17B37, 37K15, ...

This is a brief and informal introduction to cluster algebras. It roughly follows the historical path of their discovery, made jointly with A. Zelevinsky. Total positivity serves as the main motivation. Mathematics Subject Classification (2000). Primary 13F60, Secondary 05E10, 05E15, 14M15, 15A23, 15B48, 20F55, 22E46.

This survey paper presents the historical development of some problems on Cayley graphs which are interesting to graph and group theorists such as Hamiltonicity or diameter problems, to computer scientists and molecular biologists such as pancake problem or sorting by reversals, to coding theorists such as the vertex reconstruction problem related to error-correcting codes but not related to Ul...

We compute the initial ideals, with respect to certain conveniently chosen term orders, of ideals of tangent cones at torus fixed points to Schubert varieties in orthogonal Grassmannians. The initial ideals turn out to be square-free monomial ideals and therefore StanleyReisner face rings of simplicial complexes. We describe these complexes. The maximal faces of these complexes encode certain s...

We give an independent set axiomatization of symplectic matroids, a large and important class of Coxeter matroids. As an application, we construct a new class of examples of symplectic matroids from graphs. As another application, we prove that symplectic matroids satisfy a certain “basis exchange property,” and we conjecture that this basis exchange property in fact characterizes symplectic ma...

Let X1, X2, . . . be independent identically distributed random elements of a compact group G. We discuss the speed of convergence of the law of the product Xl · · ·X1 to the Haar measure. We give poly-log estimates for certain finite groups and for compact semi-simple Lie groups. We improve earlier results of Solovay, Kitaev, Gamburd, Shahshahani and Dinai. 2010 Mathematics Subject Classificat...