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677
Lecture Hall Partitions 2
, 1997
"... For a nondecreasing integer sequence a = (a 1 ; : : : ; an ) we define L a to be the set of ntuples of integers = ( 1 ; : : : ; n ) satisfying 0 1 a1 2 a2 : : : n an : This generalizes the socalled lecture hall partitions, corresponding to a i = i and previously studied by the authors ..."
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Cited by 4 (1 self)
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For a nondecreasing integer sequence a = (a 1 ; : : : ; an ) we define L a to be the set of ntuples of integers = ( 1 ; : : : ; n ) satisfying 0 1 a1 2 a2 : : : n an : This generalizes the socalled lecture hall partitions, corresponding to a i = i and previously studied by the authors
Lecture Hall Partitions
 Ramanujan J
, 1997
"... We prove a finite version of the wellknown theorem that says that the number of partitions of an integer N into distinct parts is equal to the number of partitions of N into odd parts. Our version says that the number of "lecture hall partitions of length n" of N equals the number of part ..."
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Cited by 24 (1 self)
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We prove a finite version of the wellknown theorem that says that the number of partitions of an integer N into distinct parts is equal to the number of partitions of N into odd parts. Our version says that the number of "lecture hall partitions of length n" of N equals the number
Lecture hall partitions and the wreath products Ck ≀ Sn
"... It is shown that statistics on the wreath product groups, Ck ≀ Sn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck ≀Sn. Finally, some new statistics on Ck ≀Sn are introduced, inspired by l ..."
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Cited by 5 (3 self)
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It is shown that statistics on the wreath product groups, Ck ≀ Sn, can be interpreted in terms of natural statistics on lecture hall partitions. Lecture hall theory is applied to prove distribution results for statistics on Ck ≀Sn. Finally, some new statistics on Ck ≀Sn are introduced, inspired
The geometry of lecture hall partitions and quadratic permutation statistics
 DMTCS Proceedings, 22nd International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2010
, 2010
"... Abstract. We take a geometric view of lecture hall partitions and antilecture hall compositions in order to settle some open questions about their enumeration. In the process, we discover an intrinsic connection between these families of partitions and certain quadratic permutation statistics. We d ..."
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Cited by 3 (2 self)
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Abstract. We take a geometric view of lecture hall partitions and antilecture hall compositions in order to settle some open questions about their enumeration. In the process, we discover an intrinsic connection between these families of partitions and certain quadratic permutation statistics. We
On qseries Identities Arising from Lecture Hall Partitions
, 2007
"... In this paper, we highlight two qseries identities arising from the “five guidelines ” approach to enumerating lecture hall partitions and give direct, qseries proofs. This requires two new finite corollaries of a qanalog of Gauss’s second theorem. In fact, the method reveals stronger results abo ..."
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Cited by 4 (2 self)
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In this paper, we highlight two qseries identities arising from the “five guidelines ” approach to enumerating lecture hall partitions and give direct, qseries proofs. This requires two new finite corollaries of a qanalog of Gauss’s second theorem. In fact, the method reveals stronger results
On the Refined Lecture Hall Theorem
"... Abstract. A lecture hall partition of length n is a sequence (λ1, λ2,..., λn) of nonnegative integers satisfying 0 ≤ λ1/1 ≤ · · · ≤ λn/n. M. BousquetMélou and K. Eriksson showed that there is an one to one correspondence between the set of all lecture hall partitions of length n and the set of ..."
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Abstract. A lecture hall partition of length n is a sequence (λ1, λ2,..., λn) of nonnegative integers satisfying 0 ≤ λ1/1 ≤ · · · ≤ λn/n. M. BousquetMélou and K. Eriksson showed that there is an one to one correspondence between the set of all lecture hall partitions of length n and the set
THE LECTURE HALL PARALLELEPIPED
"... The slecture hall polytopes Ps are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and BousquetMélou. We define a halfopen parallelopiped Pars associated with Ps and give a simple description of its integer points. ..."
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The slecture hall polytopes Ps are a class of integer polytopes defined by Savage and Schuster which are closely related to the lecture hall partitions of Eriksson and BousquetMélou. We define a halfopen parallelopiped Pars associated with Ps and give a simple description of its integer points
Lecture Hall Theorems, QSeries And Truncated Objects
"... We show here that the re ned theorems for both lecture hall partitions and antilecture hall compositions can be obtained as straightforward consequences of two qChu Vandermonde identities, once an appropriate recurrence is derived. We use this approach to get new lecture halltype theorems for tru ..."
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Cited by 7 (6 self)
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We show here that the re ned theorems for both lecture hall partitions and antilecture hall compositions can be obtained as straightforward consequences of two qChu Vandermonde identities, once an appropriate recurrence is derived. We use this approach to get new lecture halltype theorems
A refinement of the Lecture Hall Theorem
, 1999
"... For n 1, let Ln be the set of lecture hall partitions of length n, that is, the set of ntuples of integers = ( 1 ; : : : ; n ) satisfying 0 1 1 2 2 \Delta \Delta \Delta n n : Let de be the partition (d 1 =1e; : : : ; dn =ne), and let o(de) denote the number of its odd parts. We show t ..."
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Cited by 4 (0 self)
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For n 1, let Ln be the set of lecture hall partitions of length n, that is, the set of ntuples of integers = ( 1 ; : : : ; n ) satisfying 0 1 1 2 2 \Delta \Delta \Delta n n : Let de be the partition (d 1 =1e; : : : ; dn =ne), and let o(de) denote the number of its odd parts. We show
Results 1  10
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677