We continue the study of the Newton polytope Pm,n of the product of all maximal minors of an m x n-matrix of indeterminates. The vertices of Pm,n are encoded by coherent matching fields A = (A z) , where z runs over all m-element subsets of columns, and each Az is a bijection z —> [m]. We show that coherent matching fields satisfy some axioms analogous to the basis exchange axiom in the matroid...

Abstract: This is the first of two articles devoted to a exposition of the generatingfunction method for computing fusion rules in affine Lie algebras. The present paper is entirely devoted to the study of the tensor-product (infinite-level) limit of fusions rules. We start by reviewing Sharp’s character method. An alternative approach to the construction of tensor-product generating functions ...

We present a new method that addresses the various deficiencies of the state-ofthe-art non-linear invariant generation methods for hybrid systems. Present approaches for non-linear invariant generation are limited to linear systems, or they relay on non scalable methods which have high complexity. Moreover, for hybrid systems with discrete transitions, differential rules, and local conditions t...

Since security and privacy problems in RFID systems have attracted much attention, numerous RFID authentication protocols have been suggested. One of the various design approaches is to use light-weight logics such as bitwise Boolean operations and addition modulo 2 between m-bits words. Because these operations can be implemented in a small chip area, that is the major requirement in RFID prot...

Algebraic cryptanalysis usually requires to recover the secret key by solving polynomial equations. Gröbner bases algorithm is a well-known method to solve this problem. However, a serious drawback exists in the Gröbner bases based algebraic attacks, namely, any information won’t be got if we couldn’t work out the Gröbner bases of the polynomial equations system. In this paper, firstly, a gener...

It is well-known that one of open problems in the theory Leibniz algebras to find asuitable generalization Lie’s third theorem which associates a (local) Lie group any Liealgebra, real or complex. turns out, this related finding an appropriate analogue Liegroup for algebras. Using notion digroup, Kinyon obtained partial solution ofthis problem, namely, class so-called split Leibnizalgebras. A d...

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We consider the set M = { ( a . 11): n bh mod.rL') of all solutions of the key equation for alternant codes, where h is the syndrome polynomial. In decoding these codes a particular solution (d. (T) E M is sought, subject to d and being relatively prime and satisfying certain degree conditions. We prove that these requirements specify (d. (T ) uniquely as the minimal element of M (analogous to ...