6 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 fractions for cycle-alternating permutations
Bishal Deb, Alan D. Sokal
A permutation is said to be cycle-alternating if it has no cycle double rises, cycle double falls or fixed points; thus each index is either a cycle valley ($Ï^{-1}(i)>i<Ï(i)…
Total positivity of some polynomial matrices that enumerate labeled trees and forests. II. Rooted labeled trees and partial functional digraphs
Xi Chen, Alan D. Sokal
We study three combinatorial models for the lower-triangular matrix with entries : two involving rooted trees on the vertex set , and one inv…
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.
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…