for an $n$-gon with vertices at points $1,2,cdots,n$, the betti numbers of its suspension, the simplicial complex that involves two more vertices $n+1$ and $n+2$, is known. in this paper, with a constructive and simple proof, wegeneralize this result to find the minimal free resolution and betti numbers of the $s$-module $s/i$ where  $s=k[x_{1},cdots, x_{n}]$ and $i$ is the associated ideal to ...

For a half-translation surface ( S , q ) $(S,q)$ the associated saddle connection complex A $\mathcal {A}(S,q)$ is simplicial where vertices are connections on with simplices spanned by sets of pairwise disjoint connections. This can be naturally regarded as an induced subcomplex arc complex. We prove that any isomorphism ? : ? ? $\phi \colon \mathcal {A}(S,q) \rightarrow {A}(S^{\prime },q^{\pr...

Abstract Let $m_1 \geq m_2 2$ be integers. We consider subsets of the product symbolic sequence space $(\{0,\ldots ,m_1-1\} \times \{0,\ldots ,m_2-1\})^{\mathbb {N}^*}$ that are invariant under action semigroup multiplicative These sets defined following Kenyon, Peres, and Solomyak using a fixed integer $q . compute Hausdorff Minkowski dimensions projection these onto an affine grid unit square...

This paper generalizes work of Lascoux and Jo zeeak-Pragacz-Weyman computing the characteristic zero Betti numbers in minimal free resolutions of ideals generated by 2 2 minors of generic matrices and generic symmetric matrices, respectively. In the case of 2 2 minors, the quotients of certain polynomial rings by these ideals are the classical Segre and quadratic Veronese subalgebras, and we co...

in this paper we study the existence of commuting regular elements, verifying the notion left (right) commuting regular elements and its properties in the groupoid g(n) . also we show that g(n) contains commuting regular subsemigroup and give a necessary and sucient condition for the groupoid g(n) to be commuting regular.

It is shown in this paper how a solution for a combinatorial problem obtained from applying the greedy algorithm is guaranteed to be optimal for those instances of the problem that, under an appropriate algebraic representation, satisfy the Cohen-Macaulay property known for rings and modules in Commutative Algebra. The choice of representation for the instances of a given combinatorial problem ...

An affine semigroup is a finitely generated subsemigroup of $(\mathbb Z_{\ge 0}^d, +)$, and numerical an with $d = 1$. A growing body recent work examines shifted families semigroups, that is, semigroups the form $M_n \langle n + r_1, \ldots, r_k \rangle$ for fixed $r_1, r_k$, one each value shift parameter $n$. It has been shown within any family size minimal presentation bounded (in fact, thi...

Let $$f_1(n), \ldots , f_k(n)$$ be polynomial functions of n. For fixed $$n\in \mathbb {N}$$ let $$S_n\subseteq the numerical semigroup generated by $$f_1(n),\ldots ,f_k(n)$$ . As n varies, we show that many invariants $$S_n$$ are eventually quasi-polynomial in n, most notably Betti numbers, but also type, genus, and size $$\Delta $$ -set. The tool use is expressibility logical system parametri...