منابع مشابه
Immanants and Finite Point Processes
Given a Hermitian, non-negativede nite kernelK and a character of the symmetric group on n letters, de ne the corresponding immanant functionK [x1; : : : ; xn ] := P ( ) Qn i=1 K(xi; x (i)), where the sum is over all permutations of f1; : : : ; ng. When is the sign character (resp. the trivial character), then K is a determinant (resp. permanent). The function K is symmetric and non-negative, a...
متن کاملRate-Distortion Theory of Finite Point Processes
We study the compression of data in the case where the useful information is contained in a set rather than a vector, i.e., the ordering of the data points is irrelevant and the number of data points is unknown. Our analysis is based on rate-distortion theory and the theory of finite point processes. We introduce fundamental information-theoretic concepts and quantities for point processes and ...
متن کاملTemperley-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 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 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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series A
سال: 2000
ISSN: 0097-3165
DOI: 10.1006/jcta.2000.3097