3 citations · 9 across the 19 of their papers we have counts for
24 papers
The incidence matrix of a -ary graph
Michela Ceria, Relinde Jurrius
In this preprint we discuss a definition of a -ary graph. Furthermore, we describe how to make an incidence matrix for it, with an eye on the corresponding -matroid.
A q-analogue of delta-matroids and related concepts
Michela Ceria, Trygve Johnsen, Relinde Jurrius
We define and study q-delta-matroids, and q-g-matroids. These objects are analogues, for finite-dimensional vector spaces over finite fields, of delta-matroids and g-matroids arisi…
On the geometry of a -arc of , q even
Michela Ceria, Francesco Pavese
In , , , let , with , be a -ar…
The -ovoids of
Michela Ceria, Francesco Pavese
In this paper we are concerned with -ovoids of the symplectic polar space , even. In particular we show the existence of an elliptic quadric of ${\rm PG}(…
Alternatives for the -matroid axioms of independent spaces, bases, and spanning spaces
Michela Ceria, Relinde Jurrius
It is well known that in q-matroids, axioms for independent spaces, bases, and spanning spaces differ from the classical case of matroids, since the straightforward q-analogue of t…
On large partial ovoids of symplectic and Hermitian polar spaces
Michela Ceria, Jan De Beule, Francesco Pavese +1
In this paper we provide constructive lower bounds on the sizes of the largest partial ovoids of the symplectic polar spaces , odd square, $q \not\equiv 0 \pmod…
The complexity of solving Weil restriction systems
Alessio Caminata, Michela Ceria, Elisa Gorla
The solving degree of a system of multivariate polynomial equations provides an upper bound for the complexity of computing the solutions of the system via Groebner bases methods.…
The direct sum of -matroids
Michela Ceria, Relinde Jurrius
For classical matroids, the direct sum is one of the most straightforward methods to make a new matroid out of existing ones. This paper defines a direct sum for -matroids, the…
On near-MDS codes and caps
Michela Ceria, Antonio Cossidente, Giuseppe Marino +1
Several classes of near-MDS codes of are described. They are obtained either by considering the intersection of an elliptic quadric ovoid and a Suzuki-Tits ovoid of…
Some hypersurfaces over finite fields, minimal codes and secret sharing schemes
Angela Aguglia, Michela Ceria, Luca Giuzzi
Linear error-correcting codes can be used for constructing secret sharing schemes; however finding in general the access structures of these secret sharing schemes and, in particul…
Weighted Subspace Designs from -Polymatroids
Eimear Byrne, Michela Ceria, Sorina Ionica +1
The Assmus-Mattson theorem gives a way to identify block designs arising from codes. This result was broadened to matroids and weighted designs. In this work we present a further t…
Constructions of New q-Cryptomorphisms
Eimear Byrne, Michela Ceria, Relinde Jurrius
In the theory of classical matroids, there are several known equivalent axiomatic systems that define a matroid, which are described as matroid cryptomorphisms. A q-matroid is a q-…
Constructions of new matroids and designs over GF(q)
Eimear Byrne, Michela Ceria, Sorina Ionica +2
A perfect matroid design (PMD) is a matroid whose flats of the same rank all have the same size. In this paper we introduce the q-analogue of a PMD and its properties. In order to…
Macaulay, Lazard and the Syndrome Variety
Michela Ceria
In this paper we consider the four syndrom varieties , i.e. the set of all error locations corresponding to errors of weight , ${\sf Z}_{ns}^\ti…
Bar Code and Janet-like division
Michela Ceria
Bar Codes are combinatorial objects encoding many properties of monomial ideals. In this paper we employ these objects to study Janet-like divisions. Given a finite set of terms U,…
Applications of Bar Code to involutive divisions and a greedy algorithm for complete sets
Michela Ceria
In this paper, we describe how to get Janet decomposition for a finite set of terms and detect completeness of that set by means of the associated Bar Code. Moreover, we explain an…
Combinatorics of ideals of points: a Cerlienco-Mureddu-like approach for an iterative lex game
M. Ceria
In 1990 Cerlienco and Mureddu gave a combinatorial iterative algorithm which, given an ordered set of points, returns the lexicographical Groebner escalier of the ideal of these po…
Combinatorics of involutive divisions
Michela Ceria
The classical involutive division theory by Janet decomposes in the same way both the ideal and the escalier. The aim of this paper, following Janet's approach, is to discuss the c…
Buchberger-Zacharias Theory of Multivariate Ore Extensions
Michela Ceria
We present Buchberger Theory and Algorithm of Gröbner bases for multivariate Ore extensions of rings presented as modules over a principal ideal domain. The algorithms are based on…
Bar code for monomial ideals
Michela Ceria
Aim of this paper is to count -dimensional stable and strongly stable ideals in and variables, given their (constant) affine Hilbert polynomial. To do so, we define the…
Buchberger-Weispfenning Theory for Effective Associative Rings
Michela Ceria
We present here a new approach for computing Gröbner bases for bilateral modules over an effective ring. Our method is based on Weispfenning notion of restricted Gröbner bases and…
A general framework for Noetherian well ordered polynomial reductions
Michela Ceria, Teo Mora, Margherita Roggero
Polynomial reduction is one of the main tools in computational algebra with innumerable applications in many areas, both pure and applied. Since many years both the theory and an e…
Term-ordering free involutive bases
Michela Ceria, Teo Mora, Margherita Roggero
In this paper, we consider a monomial ideal J in P := A[x1,...,xn], over a commutative ring A, and we face the problem of the characterization for the family Mf(J) of all homogeneo…
A simplified version of the "Axis of Evil Theorem" for distinct points
Michela Ceria
Given a finite set of distinct points, Marinari-Mora's 'Axis of Evil Theorem' states that a combinatorial algorithm and interpolation enable to find a 'linear' factori…