Results 21 to 30 of about 76 (75)
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
A family of partitions with attached parts and 'N copies of N'
, 2015 in this paper we find two distinct combinatorial interpretations for a family of summations with several free parameters. In one case we used partitions with attached parts and in the other partitions with 'N copies of N'.
Mondek, P, Santos, JPO
core +1 more source
New congruences Modulo 5 and 9 for partitions with odd parts distinct
, 2021 Let pod(n) denote the number of partitions of an integer n wherein the odd parts are distinct. Recently, a number of congruences for pod(n) have been established.
Xue, Fanggang +2 more
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 +3 more
wiley +1 more source
A note on λ-analogue of Lah numbers and λ-analogue of r-Lah numbers
Demonstratio MathematicaIn 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, SigmaWe 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
The Number of Parts of Given Multiplicity in a Random Integer Partition [PDF]
, 2007 2000 Mathematics Subject Classification: 05A16, 05A17.Let Xm,n denote the number of parts of multiplicity m in a random partition of the positive integer n.
Kamenov, Emil
core
Measures and generalizations of dual Littlewood identities
Forum of Mathematics, SigmaWe introduce three families of vectors |λ―so⟩ $|\underline {\lambda }^{so}\rangle $ vertical bar lamda underbar Superscript s o Baseline right angle bracket , |λ―sp⟩ $|\underline {\lambda }^{sp}\rangle $ vertical bar lamda underbar Superscript s
Zhongren Cai +4 more
doaj +1 more source
Hyperbinary partitions and q-deformed rationals
Forum of Mathematics, SigmaA 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 +2 more
doaj +1 more source