We consider families of skew-symmetric matrices depending analytically on parameters. obtain necessary existence conditions and find normal forms for such families. The results obtained are generalized to the case possessing evenness or oddness property in totality variables.

This article studies a family of multivariate skew-symmetric distributions. We show that any multivariate probability density function admits a skewsymmetric representation. We derive several characteristics of this representation and establish an invariance property. We present a stochastic representation of skew-symmetric distributions which lends itself readily to simulations. The flexibilit...

This article was originally published in Russian in ”Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods. Part 2” (A. M. Vershik, ed.), Zapiski Nauchnyh Seminarov POMI 240 (1997), 115–135 (this text in Russian is available via http://www.pdmi.ras.ru/znsl/1997/v240.html). As it was mentioned in the ”Journal-Ref” field this English translation was published in Journal ...

We introduce the maximumskew-symmetric ow problem which generalizes ow and matching problems. We develop a theory of skew-symmetric ows that is parallel to the classical ow theory. We use the newly developed theory to extend, in a natural way, the blocking ow method of Dinitz to the skew-symmetric ow case. In the special case of the skew-symmetric ow problem that corresponds to cardinality matc...

Matrices with a skew-symmetric part of low rank arise in many applications, including path following methods and integral equations. This paper explores the properties of the Arnoldi process when applied to such a matrix. We show that an orthogonal Krylov subspace basis can be generated with short recursion formulas and that the Hessenberg matrix generated by the Arnoldi process has a structure...

Strong starters and skew starters have been widely used in various combinatorial designs. In particular skew balanced starters and symmetric skew balanced starters are crucially used in the construction of completely balanced Howell rotations. Let n = 2mfc + 1 be an odd prime power where m > 2 and k is an odd number. The existence of symmetric skew balanced starters for GF(n) has been proved fo...

A conformal partition function Pm n (s), which arose in the theory of Diophantine equations supplemented with additional restrictions, is concerned with self-dual symmetric polynomials – reciprocal R {m} Sn and skew-reciprocal S {m} Sn algebraic polynomials based on the polynomial invariants of the symmetric group Sn. These polynomials form an infinite commutative semigroup. Real solutions λn(x...