Results 11 to 20 of about 111,861 (267)
From m-clusters to m-noncrossing partitions via exceptional sequences [PDF]
, 2011 Let W be a finite crystallographic reflection group. The generalized Catalan number of W coincides both with the number of clusters in the cluster algebra associated to W, and with the number of noncrossing partitions for W.
Buan, Aslak Bakke +2 more
core +3 more sources
Growing and Destroying Catalan-Stanley Trees [PDF]
, 2018 Stanley lists the class of Dyck paths where all returns to the axis are of odd length as one of the many objects enumerated by (shifted) Catalan numbers.
Hackl, Benjamin, Prodinger, Helmut
core +2 more sources
The NADPH oxidase NOX4 regulates redox and metabolic homeostasis preventing HCC progression
Hepatology, EarlyView., 2022 Loss of NOX4 in HCC tumor cells induces metabolic reprogramming in a Nrf2/MYC‐dependent manner to promote HCC progression. Abstract Background and Aims The NADPH oxidase NOX4 plays a tumor‐suppressor function in HCC. Silencing NOX4 confers higher proliferative and migratory capacity to HCC cells and increases their in vivo tumorigenic potential in ...
Irene Peñuelas‐Haro +14 more
wiley +1 more source
Cores with distinct parts and bigraded Fibonacci numbers
, 2017 The notion of $(a,b)$-cores is closely related to rational $(a,b)$ Dyck paths due to Anderson's bijection, and thus the number of $(a,a+1)$-cores is given by the Catalan number $C_a$.
Paramonov, Kirill
core +1 more source
, 2017 Fix an integer partition lambda that has no more than n parts. Let beta be a weakly increasing n-tuple with entries from {1,..,n}. The flagged Schur function indexed by lambda and beta is a polynomial generating function in x_1, .., x_n for certain ...
Proctor, Robert A., Willis, Matthew J.
core +1 more source
Two proofs of the $q,t$-symmetry of the generalized $q,t$-Catalan number $C_{(k_1,k_2,k_3)}(q,t)$ [PDF]
, 2021 Guoce Xin, Yingrui Zhang
openalex +2 more sources
Intersection Numbers on Fibrations and Catalan Numbers
Experimental Mathematics, 2023 On an elliptic surface or threefold, Catalan numbers appear when one tries to compute the autoequivalence group action on the Bridgeland stability manifold. We explain why this happens by identifying a class of equations in the Chow ring of a fibration, where the solutions always involve Catalan numbers.
Rimma Hämäläinen +2 more
openaire +2 more sources
Generalized compositions with a fixed number of parts [PDF]
, 2010 We investigate compositions of a positive integer with a fixed number of parts, when there are several types of each natural number. These compositions produce new relationships among binomial coefficients, Catalan numbers, and numbers of the Catalan ...
Janjic, Milan
core
Tumor mutational burden as a determinant of metastatic dissemination patterns
Molecular Oncology, EarlyView.This study performed a comprehensive analysis of genomic data to elucidate whether metastasis in certain organs share genetic characteristics regardless of cancer type. No robust mutational patterns were identified across different metastatic locations and cancer types.
Eduardo Candeal +4 more
wiley +1 more source
Targeting p38α in cancer: challenges, opportunities, and emerging strategies
Molecular Oncology, EarlyView.p38α normally regulates cellular stress responses and homeostasis and suppresses malignant transformation. In cancer, however, p38α is co‐opted to drive context‐dependent proliferation and dissemination. p38α also supports key functions in cells of the tumor microenvironment, including fibroblasts, myeloid cells, and T lymphocytes.
Angel R. Nebreda
wiley +1 more source