We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, give...

It is well known due to Hahn and Mazurkiewicz that every Peano continuum a continuous image of the unit interval. We prove an assignment, which takes as input produces output mapping whose range continuum, can be realized in Borel measurable way. Similarly, we find assignment any nonempty compact metric space assigns from Cantor set onto space. To this end use Burgess selection theorem. Finally...

1 Gene tree discordance generates patterns of diminishing convergence over time Fábio K. Mendes, Yoonsoo Hahn , Matthew W. Hahn Department of Biology, Indiana University, Bloomington, IN, 47405, USA 5 Department of Life Science, Research Center for Biomolecules and Biosystems, Chung-Ang University, Seoul 06974, Republic of Korea School of Informatics and Computing, Indiana University, Bloomingt...