منابع مشابه
Cell transfer and monomial positivity
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomialpositivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include, for example, genera...
متن کاملec 2 00 6 CELL TRANSFER AND MONOMIAL POSITIVITY
We give combinatorial proofs that certain families of differences of products of Schur functions are monomial-positive. We show in addition that such monomial-positivity is to be expected of a large class of generating functions with combinatorial definitions similar to Schur functions. These generating functions are defined on posets with labelled Hasse diagrams and include for example generat...
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Let F be a flock of the quadratic cone Q: X 2=X1X3 , in PG(3, q), q even, and let 6t : X0 =xt X1 + t X2 +zt X3 , t # Fq , be the q planes defining the flock F. A flock is equivalent to a herd of ovals in PG(2, q), q even, and to a flock generalized quadrangle of order (q, q). We show that if the herd contains a monomial oval, this oval is the Segre oval. This implies a result on the existence o...
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In this paper, we devise two algorithms for the problem of testing q-monomials of degree k in any multivariate polynomial represented by a circuit, regardless of the primality of q. One is an O(2) time randomized algorithm. The other is an O(12.8) time deterministic algorithm for the same q-monomial testing problem but requiring the polynomials to be represented by tree-like circuits. Several a...
متن کاملMonomial Ideals and Duality
These are lecture notes, in progress, on monomial ideals. The point of view is that monomial ideals are best understood by drawing them and looking at their corners, and that a combinatorial duality satisfied by these corners, Alexander duality, is key to understanding the more algebraic duality theories at play in algebraic geometry and commutative algebra. Sections written so far cover Alexan...
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2007
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-006-0054-z