منابع مشابه
Unimodality via Kronecker Products
We present new proofs and generalizations of unimodality of the q-binomial coefficients ( n k ) q as polynomials in q. We use an algebraic approach by interpreting the differences between numbers of certain partitions as Kronecker coefficients of representations of Sn. Other applications of this approach include strict unimodality of the diagonal q-binomial coefficients and unimodality of certa...
متن کاملKronecker coefficients: the tensor square conjecture and unimodality
We consider two aspects of Kronecker coefficients in the directions of representation theory and combinatorics. We consider a conjecture of Jan Saxl stating that the tensor square of the Sn-irreducible representation indexed by the staircase partition contains every irreducible representation of Sn. We present a sufficient condition allowing to determine whether an irreducible representation is...
متن کاملConstruction of Multivariate Tight Frames via Kronecker Products
Integer-translates of compactly supported univariate refinable functions φi , such as cardinal B-splines, have been used extensively in computational mathematics. Using certain appropriate direction vectors, the notion of (multivariate) box splines can be generalized to (non-tensor-product) compactly supported multivariate refinable functions from the φi ’s. The objective of this paper is to in...
متن کاملKronecker Products and BIBDs
Recursive constructions are given which permit, under conditions described in the paper, a (v, b, r, k, lambda)configuration to be used to obtain a (v', b', r', k, lambda)-configuration. Although there are many equivalent definitions we will mean by a (v, b, r, k, lambda)-configuration or BIBD that (0, 1)-matrix A of size v x b with row sum r and column sum k satisfying AAT = (r lambda)I + lamb...
متن کاملUnimodality via Alternating Gamma Vectors
For a polynomial with palindromic coefficients, unimodality is equivalent to having a nonnegative g-vector. A sufficient condition for unimodality is having a nonnegative γ-vector, though one can have negative entries in the γ-vector and still have a nonnegative g-vector. In this paper we provide combinatorial models for three families of γ-vectors that alternate in sign. In each case, the γ-ve...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2014
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-014-0520-y