In the framework of Polynomial Eigenvalue Problems (PEPs), most matrix polynomials arising in applications are structured (namely, (skew-)symmetric, (skew-)Hermitian, (anti-)palindromic, or alternating). The standard way to solve PEPs is by means linearizations. frequently used linearizations belong general constructions, valid for all a fixed degree, known as companion It well known, however, ...

Very recently, we proposed the row-monomial distributed orthogonal space-time block codes (DOSTBCs) and showed that the row-monomial DOSTBCs achieved approximately twice higher bandwidth efficiency than the repetitionbased cooperative strategy [1]. However, we imposed two limitations on the row-monomial DOSTBCs. The first one was that the associated matrices of the codes must be row-monomial. T...

Convex hulls of monomials have been widely studied in the literature, and monomial convexifications are implemented in global optimization software for relaxing polynomials. However, there has been no study of the error in the global optimum from such approaches. We give bounds on the worst-case error for convexifying a monomial over subsets of [0, 1]. This implies additive error bounds for rel...

We give a new method to construct minimal free resolutions of all monomial ideals. This relies on two concepts: one is the well-known lcm-lattice ideal; other concept called Taylor basis, which describes how resolution can be embedded in resolution. An approximation formula for ideals also obtained.

We describe new fast algorithms for evaluation and interpolation on the “novel” polynomial basis over finite fields of characteristic two introduced by Lin et al. (2014). Fast are also described converting between their monomial basis, as well to from Newton associated with points algorithms. Combining yields a truncated additive Fourier transform (FFT) inverse FFT which improve upon some previ...

Divide-and-conquer method for interpolation in Guruswami-Sudan (GS) list decoding algorithm is considered. It is shown that the Groebner basis (GB) of the ideal of bivariate interpolation polynomials (IP) can be obtained as a product of trivariate polynomials corresponding to disjoint subsets of interpolation points. The impact of monomial ordering on the interpolation complexity is studied.

In this article we study bases for projective monomial curves and the relationship between the basis and the set of generators for the defining ideal of the curve. We understand this relationship best for curves in P and for curves defined by an arithmetic progression. We are able to prove that the latter are set theoretic complete intersections.

Motivated by Stanley's conjecture on the multiplication of Jack symmetric functions, we prove a couple identities showing that skew functions are semi-invariant up to translation and rotation $\pi$ angle diagram. It follows that, in some special cases, coefficients with respect basis monomial polynomials nonnegative integer coefficients.

In the vector space of symmetric functions, elements basis elementary functions are (up to a factor) chromatic disjoint unions cliques. We consider their graph complements, $\{r_{\lambda}: \lambda \text{ an integer partition}\}$ defined as complete multipartite graphs. This was first introduced by Penaguiao [21]. provide combinatorial interpretation for coefficients change-of-basis formula betw...