6 papers
Cyclic sieving phenomena via combinatorics of continued fractions
Bishal Deb
We will exhibit several instances of the cyclic sieving phenomenon involving statistics and involutions on the following combinatorial families of objects: permutations, set partit…
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 using a Laguerre digraph interpretation of the Foata--Zeilberger bijection and its variants
Bishal Deb
In the combinatorial theory of continued fractions, the Foata--Zeilberger bijection and its variants have been extensively used to derive various continued fractions enumerating se…
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)…
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…