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- W1798325575 abstract "Michael Somos conjectured a relation between Hankel determinants whose entries ${1over 2n+1}{3nchoose n}$ count ternary trees and the number of certain plane partitions and alternating sign matrices. Tamm evaluated these determinants by showing that the generating function for these entries has a continued fraction that is a special case of Gauss's continued fraction for a quotient of hypergeometric series. We give a systematic application of the continued fraction method to a number of similar Hankel determinants. We also describe a simple method for transforming determinants using the generating function for their entries. In this way we transform Somos's Hankel determinants to known determinants, and we obtain, up to a power of $3$, a Hankel determinant for the number of alternating sign matrices. We obtain a combinatorial proof, in terms of nonintersecting paths, of determinant identities involving the number of ternary trees and more general determinant identities involving the number of $r$-ary trees." @default.
- W1798325575 created "2016-06-24" @default.
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- W1798325575 date "2006-06-12" @default.
- W1798325575 modified "2023-10-16" @default.
- W1798325575 title "The Generating Function of Ternary Trees and Continued Fractions" @default.
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- W1798325575 doi "https://doi.org/10.37236/1079" @default.
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