Anti-Lecture Hall Compositions
نویسندگان
چکیده
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
منابع مشابه
On q-series Identities Arising from Lecture Hall Partitions
In this paper, we highlight two q-series 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 q-analog of Gauss’s second theorem. In fact, the method reveals stronger results about lecture hall partitions and anti-lecture hall compositions that are only partially explained com...
متن کاملLecture hall theorems, q-series and truncated objects
We show here that the refined theorems for both lecture hall partitions and anti-lecture hall compositions can be obtained as straightforward consequences of two q-Chu Vandermonde identities, once an appropriate recurrence is derived. We use this approach to get new lecture hall-type theorems for truncated objects. The truncated lecture hall partitions are sequences (λ1, . . . , λk) such that λ...
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 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 کاملEnumeration of Sequences Constrained by the Ratio of Consecutive Parts
Recurrences are developed to enumerate any family of nonnegative integer sequences λ = (λ1, . . . , λn) satisfying the constraints: λ1 a1 ≥ λ2 a2 ≥ · · · ≥ λn−1 an−1 ≥ λn an ≥ 0, for a given constraint sequence a = [a1, . . . , an] of positive integers. They are applied to derive new counting formulas, to reveal new relationships between families, and to give simple proofs of the truncated lect...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Discrete Mathematics
دوره 263 شماره
صفحات -
تاریخ انتشار 2003