On the Number of Partition Weights with Kostka Multiplicity One

On the Number of Partition Weights with Kostka Multiplicity One

Given a positive integer n, and partitions λ and μ of n, let Kλμ denote the Kostka number, which is the number of semistandard Young tableaux of shape λ and weight μ. Let J(λ) denote the number of μ such that Kλμ = 1. By applying a result of Berenshtein and Zelevinskii, we obtain a formula for J(λ) in terms of restricted partition functions, which is recursive in the number of distinct part siz...

Kostka multiplicity one for multipartitions

If [λ(j)] is a multipartition of the positive integer n (a sequence of partitions with total size n), and μ is a partition of n, we study the number K[λ(j)]μ of sequences of semistandard Young tableaux of shape [λ(j)] and total weight μ. We show that the numbers K[λ(j)]μ occur naturally as the multiplicities in certain permutation representations of wreath products. The main result is a set of ...

The modular number , the congruence number , and multiplicity one ∗

On vector partition functions with negative weights

We introduce the notion of weights into the vector partition function and the volume function associated to a sequence of vectors. We prove an explicit formula for the volume function with possibly negative weights. It is a generalization of a formula given by Brion and Vergne in [2].

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در فصل اول این پایاین نامه در خصوص تاریخ کشور اذربایجان قبل و بعد از جدایی این کشور از ایران مورد بررسی قرار گرفته است ودر فصل دوم تحولات سیاسی این کشور بعد از 1991 و در واقع بعد از فروپاشی شوروی و دولتهایی که روی کار امدند در از جمله دولت ابولفضل ایلچی بیگ،دولت حیدر علی اف وبعد از او پسرش الهام علی اف و نگرش هرکدام از این دولتها به سیاسیت خارجی اذربایجان مورد اشاره قرار گرفته است.در ودر فصل سو...