5 citations · 27 across the 26 of their papers we have counts for
28 papers
Network pearls climb stairs: a new game on graphs and its optimal solution
Ricky Xiao-Feng Chen
Let be a graph, and and be integers. Suppose there are infinite number of stairs, numbering level , level , etc. How do you place every vertex of the graph on…
Exact enumeration of RNA secondary structures by helices and loops
Ricky X. F. Chen, Christian M. Reidys, Michael S. Waterman
Enumerative studies of RNA secondary structures were initiated four decades ago by Waterman and his coworkers. Since then, RNA secondary structures have been explored according to…
Hurwitz numbers with completed cycles and Gromov--Witten theory relative to at most three points
Ricky X. F. Chen, Zhen-Ran Wang
Hurwitz numbers with completed cycles are standard Hurwitz numbers with simple branch points replaced by completed cycles. In fact, simple branch points correspond to completed …
Towards studying the structure of triple Hurwitz numbers
Ricky Xiao-Feng Chen
Going beyond the studies of single and double Hurwitz numbers, we report some progress towards studying Hurwitz numbers which correspond to ramified coverings of the Riemann sphere…
The Harer-Zagier and Jackson formulas and new results for one-face bipartite maps
Ricky X. F. Chen
The study of bipartite maps (or Grothendieck's dessins d'enfants) is closely connected with geometry, mathematical physics and free probability. Here we study these objects from th…
The minimum number of chains in a noncrossing partition of a poset
Ricky X. F. Chen
The notion of noncrossing partitions of a partially ordered set (poset) is introduced here. When the poset in question is with the complete order of natural…
On products of permutations with the most uncontaminated cycles by designated labels
Ricky X. F. Chen
There is a growing interest in studying the distribution of certain labels in products of permutations since the work of Stanley addressing a conjecture of Bóna. This paper is conc…
New equidistributions on plane trees and decompositions of -avoiding permutations
Zi-Wei Bai, Ricky X. F. Chen
Our main results in this paper are new equidistributions on plane trees and -avoiding permutations, two closely related objects. As for the former, we discover a characteristi…
Independent decisions collectively producing a long information dissemination path with a foreseen lower-bounded length in a network
Ricky X. F. Chen
Our research problems can be understood with the following metaphor: In Facebook or Twitter, suppose Mike decides to send a message to a friend Jack, and Jack next decides to pass…
A versatile combinatorial approach of studying products of long cycles in symmetric groups
Ricky X. F. Chen
In symmetric groups, studies of permutation factorizations or triples of permutations satisfying certain conditions have a long history. One particular interesting case is when two…
Combinatorially refine a Zagier-Stanley result on products of permutations
Ricky X. F. Chen
In this paper, we enumerate the pairs of permutations that are long cycles and whose product has a given cycle-type. Our main result is a simple relation concerning the desired num…
Separation probabilities and analogues of a Zagier-Stanley formula
Ricky X. F. Chen
In this paper, we first obtain some analogues of a formula of Zagier (1995) and Stanley (2011). For instance, we prove that the number of pairs of -cycles whose product has …
A refinement of the formula for -ary trees and the Gould-Vandermonde's convolution
Ricky X. F. Chen
In this paper, we present an involution on some kind of colored -ary trees which provides a combinatorial proof of a combinatorial sum involving the generalized Catalan numbers…
Lcm-lattice, Taylor Bases and Minimal Free Resolutions of a Monomial ideal
Ri-Xiang Chen
We use the lcm-lattice of a monomial ideal to study its minimal free resolutions. A new concept called a Taylor basis of a minimal free resolution is introduced and then used throu…
D-chain tomography of networks: a new structure spectrum and an application to the SIR process
Ricky X. F. Chen, Christian M. Reidys, Andrei C. Bura
The analysis of the dynamics on complex networks is closely connected to structural features of the networks. Features like, for instance, graph-cores and node degrees have been st…
Garden-of-Eden states and fixed points of monotone dynamical systems
Ricky X. F. Chen, Henning S. Mortveit, Christian M. Reidys
In this paper we analyze Garden-of-Eden (GoE) states and fixed points of monotone, sequential dynamical systems (SDS). For any monotone SDS and fixed update schedule, we identify a…
A Brief Introduction to Shannon's Information Theory
Ricky X. F. Chen
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts…
On a lower bound for sorting signed permutations by reversals
Andrei C. Bura, Ricky X. F. Chen, Christian M. Reidys
Computing the reversal distances of signed permutations is an important topic in Bioinformatics. Recently, a new lower bound for the reversal distance was obtained via the plane pe…
On the local genus distribution of graph embeddings
Ricky X. F. Chen, Christian M. Reidys
The -cell embeddings of graphs on closed surfaces have been widely studied. It is well known that (-cell) embedding a given graph on a closed orientable surface is equiva…
New formulas counting one-face maps and Chapuy's recursion
Ricky X. F. Chen, Christian M. Reidys
In this paper, we begin with the Lehman-Walsh formula counting one-face maps and construct two involutions on pairs of permutations to obtain a new formula for the number …
Linear sequential dynamical systems, incidence algebras, and Möbius functions
Ricky X. F. Chen, Christian M. Reidys
A sequential dynamical system (SDS) consists of a graph, a set of local functions and an update schedule. A linear sequential dynamical system is an SDS whose local functions are l…
A simple framework on sorting permutations
Ricky X. F. Chen, Christian M. Reidys
In this paper we present a simple framework to study various distance problems of permutations, including the transposition and block-interchange distance of permutations as well a…
Variation of the local topological structure of graph embeddings
Ricky X. F. Chen, Christian M. Reidys
The -cell embeddings of graphs on closed surfaces have been widely studied. It is well known that (-cell) embedding a given graph on a closed orientable surface is equiva…
Plane permutations and applications to a result of Zagier-Stanley and distances of permutations
Ricky X. F. Chen, Christian M. Reidys
In this paper, we introduce plane permutations, i.e. pairs where is an -cycle and is an arbitrary permutation, represented as a two-row array. Accor…