منابع مشابه
Temperley-lieb Immanants
We use the Temperley-Lieb algebra to define a family of totally nonnegative polynomials of the form ∑ σ∈Sn f(σ)x1,σ(1) · · ·xn,σ(n). The cone generated by these polynomials contains all totally nonnegative polynomials of the form ∆J,J′(x)∆L,L′(x)−∆I,I′(x)∆K,K′ (x), where ∆I,I′(x), . . . ,∆K,K′(x) are matrix minors. We also give new conditions on the eight sets I, . . . ,K ′ which characterize d...
متن کاملA2-web immanants
Abstract. We describe the rank 3 Temperley-Lieb-Martin algebras in terms of Kuperberg’s A2-webs. We define consistent labelings of webs, and use them to describe the coefficients of decompositions into irreducible webs. We introduce web immanants, inspired by Temperley-Lieb immanants of Rhoades and Skandera. We show that web immanants are positive when evaluated on totally positive matrices, an...
متن کاملProperties of the Dual Cone of Monomial-positive Immanants
We investigate a cone in the symmetric group algebra introduced by Stembridge [2]. It is dual to the cone of monomial-positive immanants of n × n matrices with indeterminate entries. We present a new set of relations between elements of the dual cone, and use these relations to show that the cone is finitely generated for n = 6, generalizing Stembridge’s result for n = 5.
متن کاملComplexity and Completeness of Immanants
Immanants are polynomial functions of n by n matrices attached to irreducible characters of the symmetric group Sn, or equivalently to Young diagrams of size n. Immanants include determinants and permanents as extreme cases. Valiant proved that computation of permanents is a complete problem in his algebraic model of NP theory, i.e., it is VNP-complete. We prove that computation of immanants is...
متن کاملThe complexity of the fermionant, and immanants of constant width
In the context of statistical physics, Chandrasekharan and Wiese recently introduced the fermionant Fermk, a determinant-like function of a matrix where each permutation π is weighted by −k raised to the number of cycles in π . We show that computing Fermk is #P-hard under polynomial-time Turing reductions for any constant k > 2, and is ⊕P-hard for k = 2, where both results hold even for the ad...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2011
ISSN: 0024-3795
DOI: 10.1016/j.laa.2011.02.029