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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 generating functions of Stanley's (P,ω)-partitions.
T.L. was supported in part by NSF DMS-0600677. 相似文献
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The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core in the monomial case as well as an efficient algorithm for computing it. We relate the core to adjoints and first coefficient ideals, and in dimension two and three we give explicit formulas. 相似文献
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《Expositiones Mathematicae》2022,40(4):920-930
We prove an asymptotic version of the Muntz–Szasz theorem, and use it to prove that all monomial operators are vanishing preserving. 相似文献
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Henrik Bresinsky Lê Tuâ n Hoa 《Proceedings of the American Mathematical Society》1999,127(5):1257-1263
The main result of the paper confirms, for generic coordinates, a conjecture which states that . Here is a homogeneous polynomial ideal in and and are the reduction numbers.
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We explicitly calculate the normal cones of all monomial primes which define the curves of the form , where . All of these normal cones are reduced and Cohen-Macaulay, and their reduction numbers are independent of the reduction. These monomial primes are new examples of integrally closed ideals for which the product with the maximal homogeneous ideal is also integrally closed.
Substantial use was made of the computer algebra packages Maple and Macaulay2.
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We introduce a method to reduce the study of the topology of a simplicial complex to that of a simpler one. Applying this
method to complexes arising from graphs, we give topological meaning to classical graph invariants. As a consequence, we answer
some questions raised in (Ehrenborg and Hetyei in Eur. J. Comb. 27(6):906–923, 2006) on the independence complex and the dominance complex of a forest and obtain improved algorithms to compute their homotopy
types. 相似文献
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Let be two monomial ideals of the polynomial ring . In this paper, we provide two lower bounds for the Stanley depth of . On the one hand, we introduce the notion of lcm number of , denoted by , and prove that the inequality holds. On the other hand, we show that , where denotes the order dimension of the lcm lattice of . We show that I and satisfy Stanley's conjecture, if either the lcm number of I or the order dimension of the lcm lattice of I is small enough. Among other results, we also prove that the Stanley–Reisner ideal of a vertex decomposable simplicial complex satisfies Stanley's conjecture. 相似文献