منابع مشابه
Anti-Lecture Hall Compositions
We study the set Ak of integer sequences = ( 1; : : : ; k), de ned by 1 1 2 2 : : : k k 0; and show that the generating function is X 2Ak q j = k Y
متن کاملAnti-lecture hall compositions and overpartitions
We show that the number of anti-lecture hall compositions of n with the first entry not exceeding k − 2 equals the number of overpartitions of n with non-overlined parts not congruent to 0,±1 modulo k. This identity can be considered as a refined version of the anti-lecture hall theorem of Corteel and Savage. To prove this result, we find two RogersRamanujan type identities for overpartition wh...
متن کاملAnti-lecture hall compositions and Andrews' generalization of the Watson-Whipple transformation
For fixed n and k, we find a three-variable generating function for the set of sequences (λ1, . . . , λn) satisfying k ≥ λ1 a1 ≥ λ2 a2 ≥ . . . ≥ λn an ≥ 0, where a := (a1, . . . , an) = (1, 2, . . . , n) or (n, n − 1, . . . , 1). When k → ∞ we recover the refined anti-lecture hall and lecture hall theorems. When a = (1, 2, . . . , n) and n → ∞, we obtain a refinement of a recent result of Chen,...
متن کاملThe Lecture Hall Parallelepiped
The s-lecture 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 Bousquet-Mélou. We define a half-open parallelopiped Pars associated with Ps and give a simple description of its integer points. We use this description to recover earlier results of Savage et al. on the δ-vector (or h∗-vector)...
متن کاملJohn L. Hall - Nobel Lecture
Four long-running currents in laser technology met and merged in 1999– 2000. Two of these were the quest toward a stable repetitive sequence of ever-shorter optical pulses and, on the other hand, the quest for the most time-stable, unvarying optical frequency possible. The marriage of UltraFastand UltraStable lasers was brokered mainly by two international teams and became exciting when a speci...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00768-9