منابع مشابه
Necessary Conditions for Schur-maximality
McNamara and Pylyavskyy conjectured precisely which connected skew shapes are maximal in the Schur-positivity order, which says that B ≤s A if sA − sB is Schurpositive. Towards this, McNamara and van Willigenburg proved that it suffices to study equitable ribbons, namely ribbons whose row lengths are all of length a or (a+ 1) for a ≥ 2. In this paper we confirm the conjecture of McNamara and Py...
متن کاملNecessary Conditions for Schur-positivity
In recent years, there has been considerable interest in showing that certain conditions on skew shapes A and B are sufficient for the difference sA − sB of their skew Schur functions to be Schur-positive. We determine necessary conditions for the difference to be Schur-positive. Our conditions are motivated by those of Reiner, Shaw and van Willigenburg that are necessary for sA = sB , and we d...
متن کاملSome Necessary Conditions for Schur Stability of Polynomials
This paper concerns the Schur stability of polynomials. Firstly necessary conditions are presented for the Schur stability of complex polynomials with fixed coefficients based on the discrete Hermite-Biehler theorem. Then the result is applied to obtain necessary conditions for the robust Schur stability of real interval polynomials.
متن کاملInformativity-based Maximality Conditions*
Von Fintel, Fox and Iatridou 2005/2012 argue that 'the NP' should not be taken to refer to the largest NP-object, as is commonly thought, but rather to the object x such that the proposition 'x satisfies NP' is maximally informative. In particular, they show that in some cases an informativity-based treatment correctly predicts that 'the NP' should refer to the smallest rather than to the large...
متن کاملAlternating Schur Series and Necessary Conditions for the Existence of Strongly Regular Graphs
Considering the Euclidean Jordan algebra of the real symmetric matrices endowed with the Jordan product and the inner product given by the usual trace of matrices, we construct an alternating Schur series with an element of the Jordan frame associated to the adjacency matrix of a strongly regular graph. From this series we establish necessary conditions for the existence of strongly regular gra...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2018
ISSN: 1077-8926
DOI: 10.37236/7524