An asymptotic formula in partition theory

Passi, Harsh A.

doi:10.1215/s0012-7094-71-03842-7

Cited by 3 publications

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“…In 1971, PAssr [2] found an asymptotic formula for log P (~), where P (~) denotes the number of partitions of $ into totally positive summands ~t, ~ in G and ~j modulo G' for some j, j= 1,2,...,l.…”

Section: Ha Passimentioning

confidence: 99%

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Asymptotic formula for distinct partitions of lattice points with congruence restrictions

Passi

1974

Monatshefte f�r Mathematik

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Section: Ha Passimentioning

confidence: 99%

“…The problem can be reduced to the special case where the lattices are integer lattices and where in fact G' is a multiple of the fundamental lattice (see sections 2,3 of [2]). This reduction makes it much easier to apply a Tauberian Theorem proved by MEI-~A~DVS, mentioned in the following section.…”

Section: Ha Passimentioning

confidence: 99%

Asymptotic formula for distinct partitions of lattice points with congruence restrictions

Passi

1974

Monatshefte f�r Mathematik

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“…In [13] there is a fairly comprehensive list of papers concerned with the asymptotic evaluation of the number of partitions of multipartites. The only investigation, of which the authors are aware, concerning multipartites subject to congruence conditions is that of Passi [8]. This paper generalizes the partition problem to lattices but obtains an asymptotic evaluation not of the number of partitions but only of its logarithm.…”

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Partitions of Large Multipartites With Congruence Conditions. I

Robertson¹,

Spencer²

1976

Transactions of the American Mathematical Society

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Partitions of large multipartites with congruence conditions. I

Robertson¹,

Spencer²

1976

Trans. Amer. Math. Soc.

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Let p ( n 1 , … , n j : A 1 , … , A j ) p({n_1}, \ldots ,{n_j}:{A_1}, \ldots ,{A_j}) be the number of partitions of ( n 1 , … , n j ) ({n_1}, \ldots ,{n_j}) where, for 1 ⩽ l ⩽ j 1 \leqslant l \leqslant j , the lth component of each part belongs to the set A l = ⋃ h ( l ) = 1 q ( l ) { a l h ( l ) + M v : v = 0 , 1 , 2 , … } {A_l} = \bigcup \nolimits _{h(l) = 1}^{q(l)} {\{ {a_{lh(l)}} + Mv :v = 0,1,2, \ldots \} } and M , q ( l ) M,q(l) and the a l h ( l ) {a_{lh(l)}} are positive integers such that 0 > a l 1 > ⋯ > a l q ( l ) ⩽ M 0 > {a_{l1}} > \cdots > {a_{lq(l)}} \leqslant M . Asymptotic expansions for p ( n 1 , … , n j : A 1 , … , A j ) p({n_1}, \ldots ,{n_j}:{A_1}, \ldots ,{A_j}) are derived, when the n l → ∞ {n_l} \to \infty subject to the restriction that n 1 ⋯ n j ⩽ n l j + 1 − ∈ {n_1} \cdots {n_j} \leqslant n_l^{j + 1 - \in } for all l, where ∈ \in is any fixed positive number. The case M = 1 M = 1 and arbitrary j was investigated by Robertson [10] while several authors between 1940 and 1960 investigated the case j = 1 j = 1 for different values of M.

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An asymptotic formula in partition theory

Cited by 3 publications

References 0 publications

Asymptotic formula for distinct partitions of lattice points with congruence restrictions

Asymptotic formula for distinct partitions of lattice points with congruence restrictions

Partitions of Large Multipartites With Congruence Conditions. I

Partitions of large multipartites with congruence conditions. I

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