413 citations · 4.6k across the 113 of their papers we have counts for
114 papers
Higher-order Stirling cycle and subset triangles: Total positivity, continued fractions and real-rootedness
Bishal Deb, Alan D. Sokal
Given a lower-triangular matrix of real numbers, one can ask the following four total-positivity questions: total positivity of the triangle itself; total positivity of its row-rev…
Thron-type continued fractions (T-fractions) for some classes of increasing trees
Veronica Bitonti, Bishal Deb, Alan D. Sokal
We introduce some classes of increasing labeled and multilabeled trees, and we show that these trees provide combinatorial interpretations for certain Thron-type continued fraction…
Continued-fraction characterization of Stieltjes moment sequences with support in
Alan D. Sokal, James Walrad
We give a continued-fraction characterization of Stieltjes moment sequences for which there exists a representing measure with support in . The proof is elementary.
Lattice paths and branched continued fractions. III. Generalizations of the Laguerre, rook and Lah polynomials
Bishal Deb, Alexander Dyachenko, Mathias Pétréolle +1
We introduce a triangular array of 5-variable homogeneous polynomials that enumerate Laguerre digraphs (digraphs in which each vertex has out-degree 0 or 1…
Coefficientwise Hankel-total positivity of the Schett polynomials
Bishal Deb, Alan D. Sokal
We prove the coefficientwise Hankel-total positivity of the even and odd subsequences of Schett polynomials .
A remark on continued fractions for permutations and D-permutations with a weight per cycle
Bishal Deb, Alan D. Sokal
We show that very simple continued fractions can be obtained for the ordinary generating functions enumerating permutations or D-permutations with a large number of independent sta…