5 citations · 17 across the 12 of their papers we have counts for
14 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…
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…
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 ()…
Classical continued fractions for some multivariate polynomials generalizing the Genocchi and median Genocchi numbers
Bishal Deb, Alan D. Sokal
A D-permutation is a permutation of satisfying and for all ; they provide a combinatorial model for the Genocchi and median Genocchi num…
Bijection between Increasing Binary Trees and Rook Placements on Double Staircases
Bishal Deb
In this paper, we shall construct a bijection between rook placements on double staircases (introduced by Josuat-Vergès in 2017) and increasing binary trees. We introduce two subcl…
Continuously Increasing Subsequences of Random Multiset Permutations
Alexander Clifton, Bishal Deb, Yifeng Huang +2
For a word and integer , we define to be the length of the longest subsequence of the form , and we let . In this paper we esti…
Coefficientwise total positivity of some matrices defined by linear recurrences
Xi Chen, Bishal Deb, Alexander Dyachenko +2
We exhibit a lower-triangular matrix of polynomials in six indeterminates that appears empirically to be coefficientwise totally positive, and which includes as a…
Chromatic Polynomial and Heaps of Pieces
Bishal Deb
Stanley in his paper [Stanley, Richard P.: Acyclic orientations of graphs In: Discrete Mathematics 5 (1973), Nr. 2, S. 171-178.] provided interpretations of the chromatic polynomia…
Multimapper: Data Density Sensitive Topological Visualization
Bishal Deb, Ankita Sarkar, Nupur Kumari +3
Mapper is an algorithm that summarizes the topological information contained in a dataset and provides an insightful visualization. It takes as input a point cloud which is possibl…