Quantifying dependence between extreme values is a central problem in many theoretical and applied studies. The main distinction is between asymptotically independent and asymptotically dependent extremes, with important theoretical examples of these general limiting classes being the extremal behaviour of a bivariate Normal distribution, for asymptotic independence, and of the bivariate t dist...

Cluster algebras are a class of commutative rings introduced by Fomin and Zelevinsky. It is well-known that these algebras are closely related with different areas of mathematics. A particular analogy exists between combinatorial aspects of cluster algebras and Kac-Moody algebras: roughly speaking, cluster algebras are associated with skew-symmetrizable matrices while Kac-Moody algebras corresp...

Using growth diagrams, we define skew domino Schensted algorithm which is a domino analogue of “Robinson-Schensted algorithm for skew tableaux” due to Sagan and Stanley. The color-to-spin property of Shimozono and White is extended. As an application, we give a simple generating function for a weighted sum of skew domino tableaux whose special case is a generalization of Stanley’s sign-imbalanc...

Using growth diagrams, we define skew domino Schensted algorithm which is a domino analogue of “Robinson-Schensted algorithm for skew tableaux” due to Sagan and Stanley. The color-to-spin property of Shimozono and White is extended. As an application, we give a simple generating function for a weighted sum of skew domino tableaux whose special case is a generalization of Stanley’s sign-imbalanc...

The Schur polynomials s ? are essential in understanding the representation theory of general linear group. They also describe cohomology ring Grassmannians. For ?=(n,n-1,?,1) a staircase shape and ??? subpartition, Stembridge equality states that ?/? =s T . This provides information about symmetry ring. stable Grothendieck G , dual g developed by Buch, Lam, Pylyavskyy, variants K-theory Using ...

An $n$-by-$n$ matrix $A$ is called symmetric, skew-symmetric, and orthogonal if $A^T=A$, $A^T=-A$, $A^T=A^{-1}$, respectively. We give necessary sufficient conditions on a complex so that it sum of type ``"orthogonal $+$ symmetric" in terms the Jordan form $A-A^T$. also "orthogonal skew-symmetric" $A+A^T$.

Abstract. In this paper, a family of skew-slash distributions is defined and investigated. We define the new family by the scale mixture of a skew-elliptically distributed random variable with the power of a uniform random variable. This family of distributions contains slash-elliptical and skew-slash distributions. We obtain the moments and some distributional properties of the new family of d...

‎‎A natural generalization of two dimensional cyclic code ($T{TDC}$) is two dimensional skew cyclic code‎. ‎It is well-known that there is a correspondence between two dimensional skew cyclic codes and left ideals of the quotient ring $R_n:=F[x,y;rho,theta]/_l$‎. ‎In this paper we characterize the left ideals of the ring $R_n$ with two methods and find the generator matrix for two dimensional s...

Robin Harte and David Larson The first author was partially supported by Enterprise Ireland grant number IC/2001/027 Abstract We offer a perturbation theory for finite ascent and descent properties of bounded operators. There are various degrees of “skew exactness” ([10];[7] (10.9.0.1), (10.9.0.2)) between compatible pairs of operators, bounded and linear between normed spaces: 1. Definition Su...