منابع مشابه
Congruences for Han’s Generating Function
For an integer t ≥ 1 and a partition λ, we let Ht(λ) be the multiset of hook lengths of λ which are divisible by t. Then, define aeven t (n) and aodd t (n) to be the number of partitions of n such that |Ht(λ)| is even or odd, respectively. In a recent paper, Han generalized the Nekrasov-Okounkov formula to obtain a generating function for at(n) = aeven t (n)− aodd t (n). We use this generating ...
متن کاملA Mthod for Generating the Turbulent Intermittency Function
A detection method based on sensitization of a squared double differentiated signal is developed which discriminates the turbulent zones from laminar zones quite accurately. The procedure adopts a variable threshold and a variable hold time of the order of the Kolmogorov time scale. The output file so generated, includes all the information for further analysis of the turbulent signal.
متن کاملCongruences for Andrews’ Spt-function
Congruences are found modulo powers of 5, 7 and 13 for Andrews’ smallest parts partition function spt(n). These congruences are reminiscent of Ramanujan’s partition congruences modulo powers of 5, 7 and 11. Recently, Ono proved explicit Ramanujan-type congruences for spt(n) modulo ` for all primes ` ≥ 5 which were conjectured earlier by the author. We extend Ono’s method to handle the powers of...
متن کاملCongruences for the Andrews spt function.
Ramanujan-type congruences for the Andrews spt(n) partition function have been found for prime moduli 5 ≤ ℓ ≤ 37 in the work of Andrews [Andrews GE, (2008) J Reine Angew Math 624:133-142] and Garvan [Garvan F, (2010) Int J Number Theory 6:1-29]. We exhibit unexpectedly simple congruences for all ℓ≥5. Confirming a conjecture of Garvan, we show that if ℓ≥5 is prime and (-δ/ℓ) = 1, then spt[(ℓ2(ℓn...
متن کاملRamanujan Type Congruences for a Partition Function
We investigate the arithmetic properties of a certain function b(n) given by ∞ ∑ n=0 b(n)qn = (q; q)−2 ∞ (q 2; q2)−2 ∞ . One of our main results is b(9n + 7) ≡ 0 (mod 9).
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: Involve, a Journal of Mathematics
سال: 2009
ISSN: 1944-4176
DOI: 10.2140/involve.2009.2.225