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...

Grabner basis is olle of the most important tools ill recent symbolic algebraic computations. Howe\'er, computing a Grobncr basis fo r the given polynomial ideal is lIot easy and it is lIot numcric.. . l1y stable if polynomials have inexact coefficients. I n this paper, we study what we should get for computing a Grabner basis with inexact coefficients alld introduce a naive method to compute a...

This is the first of two articles devoted to a comprehensive exposition of the generating-function 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 consider thus in detail the problem of constructing tensor-product generating functions in finite Lie algebras. From the be...

Plato in Theory of Philosopher-King believes that all of the members of ideal city-state, whether ruler or citizens, will attain happiness if the philosopher is the ruler. But there are paradoxes in the theory and the bases of the happiness are unstable too. In other words, Plato in his theory presents hierarchical dualities (Intelligible/Visible world, Episteme/ Doxa,True/ Untrue Or Shadow, …)...

Expansions in noninteger bases often appear in number theory and probability theory, and they are closely connected to ergodic theory, measure theory and topology. For two-letter alphabets the golden ratio plays a special role: in smaller bases only trivial expansions are unique, whereas in greater bases there exist nontrivial unique expansions. In this paper we determine the corresponding crit...