Congruences for restricted plane overpartitions modulo 4 and 8
نویسندگان
چکیده
منابع مشابه
Plane overpartitions and cylindric partitions
Generating functions of plane overpartitions are obtained using various methods: non–intersecting paths, RSK type algorithms and symmetric functions. We extend some of the results to cylindric partitions. Also, we show that plane overpartitions correspond to domino tilings and we give some basic properties of this correspondence.
متن کاملOverpartitions with Restricted Odd Differences
We use q-difference equations to compute a two-variable q-hypergeometric generating function for overpartitions where the difference between two successive parts may be odd only if the larger part is overlined. This generating function specializes in one case to a modular form, and in another to a mixed mock modular form. We also establish a two-variable generating function for the same overpar...
متن کاملCongruences modulo Prime Powers
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f (x) ∈ Z[x]. We establish the congruence p deg f k≡r (mod p α) n k (−1) k f k − r p α ≡ 0 mod p ∞ i=α ⌊n/p i ⌋ (motivated by a conjecture arising from algebraic topology), and obtain the following vast generalization of Lucas' theorem: If α > 1 and l, s, t are nonnegative integers with s, t < p, then 1 ⌊n/p α−1 ⌋! k≡r (...
متن کاملAn Infinite Family of Congruences for `-regular Overpartitions
We consider new properties of the combinatorial objects known as overpartitions (which are natural generalizations of integer partitions). In particular, we establish an infinite set of Ramanujan-type congruences for the restricted overpartitions known as `-regular overpartitions. This significantly extends the recent work of Shen which focused solely on 3–regular overpartitions and 4–regular o...
متن کاملCombinatorial Congruences modulo Prime Powers
Let p be any prime, and let α and n be nonnegative integers. Let r ∈ Z and f(x) ∈ Z[x]. We establish the congruence p f ∑ k≡r (mod pα) (n k ) (−1)f ( k − r pα ) ≡ 0 ( mod p ∑∞ i=α n/p i ) (motivated by a conjecture arising from algebraic topology) and obtain the following vast generalization of Lucas’ theorem: If α is greater than one, and l, s, t are nonnegative integers with s, t < p, then 1 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Ramanujan Journal
سال: 2018
ISSN: 1382-4090,1572-9303
DOI: 10.1007/s11139-018-0036-5