[HTML][HTML] Polyocollection ideals and primary decomposition of polyomino ideals
In this article, we study the primary decomposition of some binomial ideals. In particular, we
introduce the concept of polyocollection, a combinatorial object that generalizes the …
introduce the concept of polyocollection, a combinatorial object that generalizes the …
Shellable simplicial complex and switching rook polynomial of frame polyominoes
R Jahangir, F Navarra - Journal of Pure and Applied Algebra, 2024 - Elsevier
Let P be a frame polyomino, a new kind of non-simple polyomino. In this paper we study the
h-polynomial of K [P] in terms of the switching rook polynomial of P using the shellable …
h-polynomial of K [P] in terms of the switching rook polynomial of P using the shellable …
On Gr\" obner bases and Cohen-Macaulay property of closed path polyominoes
In this paper we introduce some monomial orders for the class of closed path polyominoes
and we prove that the set of the generators of the polyomino ideal attached to a closed path …
and we prove that the set of the generators of the polyomino ideal attached to a closed path …
Hilbert–Poincaré series and Gorenstein property for some non-simple polyominoes
Let P be a closed path having no zig-zag walks, a kind of non-simple thin polyomino. In this
paper, we give a combinatorial interpretation of the h-polynomial of K [P], showing that it is …
paper, we give a combinatorial interpretation of the h-polynomial of K [P], showing that it is …
Hilbert series of simple thin polyominoes
G Rinaldo, F Romeo - Journal of Algebraic Combinatorics, 2021 - Springer
Let PP be a simple thin polyomino, namely a polyomino that has no holes and does not
contain a square tetromino as a subpolyomino. In this paper, we determine the reduced …
contain a square tetromino as a subpolyomino. In this paper, we determine the reduced …
Primality of polyomino ideals by quadratic Gröbner basis
In this work, we provide a necessary and sufficient condition on a polyomino ideal for having
the set of inner 2‐minors as graded reverse lexicographic Gröbner basis, due to …
the set of inner 2‐minors as graded reverse lexicographic Gröbner basis, due to …
Regularity and Gorenstein property of the -convex Polyominoes
We study the coordinate ring of an $ L $-convex polyomino, determine its regularity in terms
of the maximal number of rooks that can be placed in the polyomino. We also characterize …
of the maximal number of rooks that can be placed in the polyomino. We also characterize …
On the rook polynomial of grid polyominoes
R Dinu, F Navarra - arXiv preprint arXiv:2309.01818, 2023 - arxiv.org
We investigate the algebraic properties of the coordinate ring of grid polyominoes. This class
of non-simple and thin polyominoes was introduced by Mascia, Rinaldo, and Romeo, but not …
of non-simple and thin polyominoes was introduced by Mascia, Rinaldo, and Romeo, but not …
Primality of closed path polyominoes
In this paper, we introduce a new class of polyominoes, called closed paths, and we study
the primality of their associated ideal. Inspired by an existing conjecture that characterizes …
the primality of their associated ideal. Inspired by an existing conjecture that characterizes …
Shellable flag simplicial complexes of non-simple polyominoes
F Navarra - arXiv preprint arXiv:2408.12367, 2024 - arxiv.org
arXiv:2408.12367v1 [math.AC] 22 Aug 2024 Page 1 Shellable flag simplicial complexes of
non-simple polyominoes Francesco Navarra1* 1*Faculty of Engineering and Natural Sciences …
non-simple polyominoes Francesco Navarra1* 1*Faculty of Engineering and Natural Sciences …