Let the sign of a skew standard Young tableau be the sign of the permutation you get by reading it row by row from left to right, like a book. We examine how the sign property is transferred by the skew Robinson-Schensted correspondence invented by Sagan and Stanley. The result is a remarkably simple generalization of the ordinary non-skew formula. The sum of the signs of all standard tableaux ...

We obtain a near-tight bound of O(n), for any ε > 0, on the complexity of the overlay of the minimization diagrams of two collections of surfaces in four dimensions. This settles a long-standing problem in the theory of arrangements, most recently cited by Agarwal and Sharir [3, Open Problem 2], and substantially improves and simplifies a result previously published by the authors [17]. Our bou...

We consider the normwise condition number and backward error of eigenvalues of matrix polynomials having ⋆-palindromic/antipalindromic and ⋆-even/odd structure with respect to structure preserving perturbations. Here ⋆ denotes either the transpose T or the conjugate transpose ∗. We show that when the polynomials are complex and ⋆ denotes complex conjugate, then to each of the structures there c...

Two skew cyclic codes can be equivalent for the Hamming metric only if they have the same length, and only the zero code is degenerate. The situation is completely different for the rank metric, where lengths of codes correspond to the number of outgoing links from the source when applying the code on a network. We study rank equivalences between skew cyclic codes of different lengths and, with...

In this paper, we study the arithmetics of skew polynomial rings over finite fields, mostly from an algorithmic point of view. We give various algorithms for fast multiplication, division and extended Euclidean division. We give a precise description of quotients of skew polynomial rings by a left principal ideal, using results relating skew polynomial rings to Azumaya algebras. We use this des...

Many techniques have been developed for detecting the dominant skew angle of printed documents [2]. However sometimes more than one skew angle is represented in the document image. Baird [3] points out that the paste-up of text columns may result in slightly (but significantly) different skew angles and notes the importance of segmenting the columns first in order that individual skew correctio...

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...

This paper aims to investigate properties of involution palindrome languages. Let θ be either a morphic or antimorphic involution. we show that if θ is an antimorphic involution, then the set of all θ-palindrome words is a proper subset of all skew θ-palindrome words. We give a characterization for that a word is skew θ-palindrome. That is, A word is skew θ-palindrome if and only if it is a pro...

We introduce the class of Beta-Wishart random matrices and develop a comprehensive eigenvalue theory for it. The Beta-Wishart matrices generalize the classical real, complex, and quaternion Wishart matrices to a unform and continuous model valid for any β > 0. As most distributions are expressed in terms of the hypergeometric function of a matrix argument, many new identities for this function ...