A Note on Andrews’ Partitions with Parts Separated by Parity
نویسندگان
چکیده
منابع مشابه
A note on partitions into distinct parts and odd parts
Bousquet-Mélou and Eriksson showed that the number of partitions of n into distinct parts whose alternating sum is k is equal to the number of partitions of n into k odd parts, which is a refinement of a well-known result by Euler. We give a different graphical interpretation of the bijection by Sylvester on partitions into distinct parts and partitions into odd parts, and show that the bijecti...
متن کاملParity Results for p-Regular Partitions with Distinct Parts
We consider the partition function bp(n), which counts the number of partitions of the integer n into distinct parts with no part divisible by the prime p. We prove the following: Let p be a prime greater than 3 and let r be an integer between 1 and p−1, inclusively, such that 24r + 1 is a quadratic nonresidue modulo p. Then, for all nonnegative integers n, bp(pn + r) ≡ 0 (mod 2).
متن کاملConjecture of Andrews on Partitions
Definition 1.2. For an even integer λ, let Aλ,k,a(n) denote the number of partitions of n into parts such that no part which is not equivalent to 0(mod λ+ 1) may be repeated and no part is equivalent to 0,±(a−λ/2)(λ+1)mod[(2k−λ+1)(λ+1)]. For an odd integer λ, let Aλ,k,a(n) denote the number of partitions of n into parts such that no part which is not equivalent to 0(mod((λ+1)/2)) may be repeate...
متن کاملCombinatorial telescoping for an identity of Andrews on parity in partitions
Following the method of combinatorial telescoping for alternating sums given by Chen, Hou and Mu, we present a combinatorial telescoping approach to partition identities on sums of positive terms. By giving a classification of the combinatorial objects corresponding to a sum of positive terms, we establish bijections that lead a telescoping relation. We illustrate this idea by giving a combinat...
متن کاملA Note on an Identity of Andrews
In this note we use the q-exponential operator technique on an identity of Andrews.
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: Annals of Combinatorics
سال: 2019
ISSN: 0218-0006,0219-3094
DOI: 10.1007/s00026-019-00440-z