Results 21 to 30 of about 829 (63)

Congruences involving F‐partition functions

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 1, Page 187-188, 1994., 1994
The primary goal of this note is to prove the congruence ϕ3(3n + 2) ≡ 0(mod3), where ϕ3(n) denotes the number of F‐partitions of n with at most 3 repetitions. Secondarily, we conjecture a new family of congruences involving cϕ2(n), the number of F‐partitions of n with 2 colors.
James Sellers
wiley   +1 more source

A new class of infinite products, and Euler′s totient

International Journal of Mathematics and Mathematical Sciences, Volume 17, Issue 3, Page 417-422, 1994., 1993
We introduce some new infinite products, the simplest being where ϕk is the set of positive integers less than and relatively prime to k, valid for |y|∧|qy| both less than unity, with q ≠ 1. The idea of a q‐analogue for the Euler totient function is suggested.
Geoffrey B. Campbell
wiley   +1 more source

Some Congruences of a Restricted Bipartition Function

, 2016
Let $c_N(n)$ denotes the number of bipartitions $(\lambda, \mu)$ of a positive integer $n$ subject to the restriction that each part of $\mu$ is divisible by $N$.
Boruah, Chayanika, Saikia, Nipen
core   +2 more sources

Partitions which are p- and q-core [PDF]

, 2001
Let p and q be distinct primes, n an integer with n > p2q2. Then there is no partition of n which is at the same time p- and q-core.
Schlage-Puchta, Jan-Christoph
core  

Use of a Cytobrush for Sampling the Ear Canal of Dogs With Otitis Externa

Veterinary Dermatology, Volume 37, Issue 2, Page 227-235, April 2026.
Cytological examination of the ear canal is essential for evaluating dogs with otitis externa (OE). The conventional sampling method uses a swab. However, the cytobrush (gynaecological cervical brush), already used for cytological collection from other anatomical sites, has not been adequately investigated for this purpose in dogs with OE.
Nicoly Radaeli Atanasio, Gabriela Reis Ledur, Danilo Marcondes Filho, Daniel Guimarães Gerardi   +3 more
wiley   +1 more source

A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers

Demonstratio Mathematica
In this study, we introduce the λ\lambda -analogue of Lah numbers and λ\lambda -analogue of rr-Lah numbers in the view of degenerate version, respectively.
Kim Taekyun, Kim Hye Kyung
doaj   +1 more source

On the proportion of derangements in affine classical groups

Forum of Mathematics, Sigma
We derive exact formulas for the proportions of derangements and of derangements of p-power order in the affine classical groups $\operatorname {\mathrm {AU}}_m(q)$ , $\operatorname {\mathrm {ASp}}_{2m}(q)$ , $\operatorname {\mathrm {AO ...
Jessica Anzanello
doaj   +1 more source

Hyperbinary partitions and q-deformed rationals

Forum of Mathematics, Sigma
A hyperbinary partition of the nonnegative integer n is a partition where every part is a power of $2$ and every power of $2$ appears at most twice.
Thomas McConville, James Propp, Bruce Sagan   +2 more
doaj   +1 more source

Congruences involving generalized Frobenius partitions

, 1992
International Journal of Mathematics and Mathematical Sciences, Volume 16, Issue 2, Page 413-415, 1993.
James Sellers
wiley   +1 more source

Unlimited parity alternating partitions

, 2018
We introduce a new type of partitions that consists of partitions whose different parts alternate in parity (e.g., $3+2+2+1+1$). Various properties of this partition function are studied.
Chern, Shane
core