Results 111 to 120 of about 9,807,843 (352)
Fuss-Catalan numbers and planar partitions [PDF]
arXiv, 2023 We show how the Fuss-Catalan numbers $ \frac{1}{p n+1}\binom{pn+1}{n}$ enter different problems of counting simple and multiple planar partitions.
arxiv
ChemElectroChem, EarlyView.This review explores the transformative role of graphene derivatives in electrochemical biosensors for diagnostics, environmental monitoring, and industrial sensing. Highlighting innovations in synthesis and covalent functionalization, it discusses how these materials enhance biosensor stability, specificity, and scalability.
Petr Jakubec +8 more
wiley +1 more source
On ideal convergence of sequences via Catalan matrix operator
Miskolc Mathematical NotesCatalan sequence initially introduced by Euler but named after Eugene Catalan has found abundant applications in the fields of probability theory, number theory, analysis, combinatorics etc.
Vakeel Ahmad Khan, Mikail Et, Umme Tuba
doaj +1 more source
Congruences from $q$-Catalan Identities [PDF]
Transactions on Combinatorics, 2016 In this paper, by studying three $q$-Catalan identities given by Andrews, we arrive at a certain number of congruences. These congruences are all modulo $Phi_n(q)$, the $n$-th cyclotomic polynomial or the related functions and modulo $q$-integers
Qing Zou
doaj +1 more source
The Super Patalan Numbers [PDF]
J. Integer Seq. 18 (2015), Article 15.3.3, 2014 We introduce the super Patalan numbers, a generalization of the super Catalan numbers in the sense of Gessel, and prove a number of properties analagous to those of the super Catalan numbers. The super Patalan numbers generalize the super Catalan numbers similarly to how the Patalan numbers generalize the Catalan numbers.
arxiv
Label‐Free Photonic Biosensors: Key Technologies for Precision Diagnostics
ChemistryEurope, EarlyView.Photonic biosensors are versatile technologies promising unique advantages to improve current diagnosis workflows. On‐going research is directed to systems integration and automation as well as enhancing assay performance. Advances in bioengineering, material sciences, and photonics engineering will be the key toward their eventual implementation as ...
Maria Soler, Laura M. Lechuga
wiley +1 more source
Caplletra: Revista Internacional de Filologia, 2014 In the last years a very important amount of immigrant students unaware of Catalan, a language typical of the educational system of Catalonia, have arrived to Catalonia.
Josep M. Serra +4 more
doaj +1 more source
Permutations avoiding an increasing number of length-increasing forbidden subsequences [PDF]
Discrete Mathematics & Theoretical Computer Science, 2000 A permutation π is said to be τ -avoiding if it does not contain any subsequence having all the same pairwise comparisons as τ . This paper concerns the characterization and enumeration of permutations which avoid a set F^j of subsequences increasing ...
Elena Barcucci +3 more
doaj +1 more source
Catalan-like numbers and Hausdorff moment sequences [PDF]
arXiv, 2018 In this paper we show that many well-known counting coefficients, including the Catalan numbers, the Motzkin numbers, the central binomial coefficients, the central Delannoy numbers are Hausdorff moment sequences in a unified approach. In particular we answer a conjecture of Liang at al. which such numbers have unique representing measures.
arxiv
Communications of the American Mathematical SocietyGiven a (bounded affine) permutation f f , we study the positroid Catalan number C f C_f defined to be the torus-equivariant Euler characteristic of the associated open positroid variety. We introduce a class of repetition-free permutations and show that the corresponding positroid Catalan numbers ...
Galashin, Pavel, Lam, Thomas
openaire +2 more sources