We show that the associated form, or, equivalently, a Macaulay inverse system, of an Artinian complete intersection of type (d, . . . , d) is polystable. As an application, we obtain an invariant-theoretic variant of the Mather-Yau theorem for homogeneous hypersurface singularities.

Abstract Private set intersection (PSI) allows two mutually distrusting parties each with a as input, to learn the of both their sets without revealing anything more about respective input sets. Traditionally, PSI studies static setting where computation is performed only once on parties’ We initiate study updatable private (UPSI), which compute regular basis that also constantly get updated. c...

‎let $r$ be a commutative ring with non-zero identity. ‎we describe all $c_3$‎- ‎and $c_4$-free intersection graph of non-trivial ideals of $r$ as well as $c_n$-free intersection graph when $r$ is a reduced ring. ‎also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎finally, ‎we shall prove that almost all artin rings $r$ have hamiltonian intersection graphs. ...

In this paper, we re-visit the problem of unconditionally secure multiparty set intersection in information theoretic model. Li et.al [24] have proposed a protocol for n-party set intersection problem, which provides unconditional security when t < n 3 players are corrupted by an active adversary having unbounded computing power. Moreover, they have claimed that their protocol takes six rounds ...

Many data mining algorithms use privacy preserving set intersection operations. Private set operations have considered semi-honest and malicious adversarial models in cryptographic settings. Protocols in semi-honest model, requiring light computations, provide weak security. Protocols in malicious model guarantee strong security at the price of expensive computations like homomorphic encryption...

The intersection graph $mathbb{Int}(A)$ of an $S$-act $A$ over a semigroup $S$ is an undirected simple graph whose vertices are non-trivial subacts of $A$, and two distinct vertices are adjacent if and only if they have a non-empty intersection. In this paper, we study some graph-theoretic properties of $mathbb{Int}(A)$ in connection to some algebraic properties of $A$. It is proved that the fi...