Splitting ring of a monic separable polynomial

On a Variant of Bertini’s Theorem and Generators of Ideals of a Polynomial Ring with Monic Polynomials

In this paper we discuss different versions of Bertini’s theorem and prove a variant of a theorem of Bertini. We also prove the following theorem. Suppose A is a semilocal regular reduced affine algebra over an algebraically closed field of characteristic zero such that every maximal ideal in A[T ] is complete intersection, with dim(A) = n > 0. Suppose I is an ideal of A[T ], with height(I) = n...

The Probability That a Random Monic p-adic Polynomial Splits

Separable Linkable Threshold Ring Signatures

A ring signature scheme is a group signature scheme with no group manager to setup a group or revoke a signer. A linkable ring signature, introduced by Liu, et al. [20], additionally allows anyone to determine if two ring signatures are signed by the same group member (a.k.a. they are linked). In this paper, we present the first separable linkable ring signature scheme, which also supports an e...

Tutte polynomial expansions for 2-separable graphs

Let Ĝ be a graph obtained from a graph G with no loops or coloops by replacing each edge e= uw of G by a connected graph He that has only the vertices u and w in common with the rest of Ĝ. Two mutually dual formulas are proved for the Tutte polynomial of Ĝ in terms of parameters of the graphs He and (in the one case) 0ow polynomials of subgraphs of G or (in the other case) tension polynomials o...

THE PROBABILITY THAT A RANDOM MONIC p-ADIC POLYNOMIAL SPLITS INTO LINEAR FACTORS

Let n be a positive integer and let p be a prime. We calculate the probability that a random monic polynomial of degree n with coefficients in the ring Zp of p-adic integers splits over Zp into linear factors.