منابع مشابه
A Mthod for Generating the Turbulent Intermittency Function
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For an integer t ≥ 1 and a partition λ, we let Ht(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define aeven t (n) and aodd t (n) to be the number of partitions of n such that |Ht(λ)| is even or odd, respectively. In a recent paper, Han generalized the Nekrasov-Okounkov formula to obtain a generating function for at(n) = aeven t (n)− aodd t (n). We use this generating ...
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We study a generating function for the sum over fatgraphs with specified valences of vertices and faces, inversely weighted by the order of their symmetry group. A compact expression is found for general (i.e. non necessarily connected) fatgraphs. This expression admits a matrix integral representation which enables to perform semi–classical computations, leading in particular to a closed formu...
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We present a natural extension of Andrews’ multiple sums counting partitions of the form (λ1, · · · , λm) with λi ≥ λi+k−1 + 2. The multiple sum that we construct is the generating function for the so-called K-restricted jagged partitions. A jagged partition is a sequence of non-negative integers (n1, n2, · · · , nm) with nm ≥ 1 subject to the weakly decreasing conditions ni ≥ ni+1− 1 and ni ≥ ...
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Polygons are described as almost-convex if their perimeter differs from the perimeter of their minimum bounding rectangle by twice their ‘concavity index’, m. Such polygons are called m-convex polygons and are characterized by having up to m indentations in their perimeter. We first describe how we conjectured the (isotropic) generating function for the case m = 2 using a numerical procedure ba...
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ژورنال
عنوان ژورنال: Turkish Journal of Analysis and Number Theory
سال: 2014
ISSN: 2333-1100
DOI: 10.12691/tjant-2-4-4