We extend the notions of quasi-monomial groups and almost monomial groups, in framework supercharacter theories, we study their connection with Artin's conjecture regarding holomorphy Artin $L$-functions.

Abstract Verifying arithmetic circuits and most prominently multiplier is an important problem which in practice still considered to be challenging. One of the currently successful verification techniques relies on algebraic reasoning. In this article, we present AMulet2 , a fully automatic tool for integer multipliers combining SAT solving computer algebra. Our models given as and-inverter gra...

We define a new combinatorial object, which we call a labeled hypergraph, uniquely associated to any square-free monomial ideal. We prove several upper bounds on the regularity of a square-free monomial ideal in terms of simple combinatorial properties of its labeled hypergraph. We also give specific formulas for the regularity of square-free monomial ideals with certain labeled hypergraphs. Fu...

When C ⊆ F is a linear code over a finite field F, every linear Hamming isometry of C to itself is the restriction of a linear Hamming isometry of F to itself, i.e., a monomial transformation. This is no longer the case for additive codes over non-prime fields. Every monomial transformation mapping C to itself is an additive Hamming isometry, but there exist additive Hamming isometries that are...

The Laplacian of an undirected graph is a square matrix, whose eigenvalues yield important information. We can regard graphs as one-dimensional simplicial complexes, and as whether there is a generalisation of the Laplacian operator to simplicial complexes. It turns out that there is, and that is useful for calculating real Betti numbers [8]. Duval and Reiner [5] have studied Laplacians of a sp...

We consider the problem of finding isolated common roots a set polynomial functions defining zero-dimensional ideal I in ring R polynomials over C. Normal form algorithms provide an algebraic approach to solve this problem. The framework presented Telen et al. (2018) uses truncated normal forms (TNFs) compute algebra structure R/I and solutions I. This allows for use much more general bases tha...

Let K be a field of characteristic 0 containing all roots of unity. We classified all the Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.  2004 Elsevier Inc. All rights reserved.

Let K be a field of characteristic 0 containing all roots of unity. We classified all the Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.

We characterize the lcm lattices that support a monomial ideal with a pure resolution. Given such a lattice, we provide a construction that yields a monomial ideal with that lcm lattice and whose minimal free resolution is pure.

Let K be a field of characteristic 0 containing all roots of unity. We classify the all Hopf structures on monomial K-coalgebras, or, in dual version, on monomial K-algebras.