My book “New Insight into Communication: from theory to practice” has received 2,000,000+ online reads from an online ICT community
4. Ricky Chen, Joseph McNitt, Henning Mortveit, Ryan Pederson, Christian Reidys, Lipschitz continuity under toric equivalence for asynchronous Boolean networks, Chaos, 33 (2023), 023118. https://doi.org/10.1063/5.0119621 .
3. Ricky Chen, Christian Reidys, Michael Waterman, RNA secondary structures with given motif specification: combinatorics and algorithms, Bulletin of Mathematical Biology, 85 (2023), Article number: 21. https://doi.org/10.1007/s11538-023-01128-5
2. Ricky Chen, Andrei Bura, Christian Reidys, D-chain tomography of networks: a new structure spectrum and an application to the SIR process, SIAM Journal on Applied Dynamical Systems, 18(4) (2019), pp. 2181–2201.
1. Ricky Chen, Christian Reidys, Linear sequential dynamical systems, incidence algebras, and Mobius functions, Linear Algebra and its Applications, Volume 553, 15 September 2018, pp. 270-291.
Sequential dynamical systems (SDS) are dynamical systems on networks, where nodes in the network update their status sequentially based on their respective local functions (update rules). Thus, the global system function is a composition of the local functions w.r.t. a specific updating schedule. Linear SDS are SDS where local functions are linear. We obtained a closed simple formula for the global system function for any given linear SDS; we also showed that, to some extent, any linear dynamical system can be sequentialized. Furthermore, we discovered a connection between linear SDS and the incidence algebras of partially ordered sets. In particular, we proved a cut theorem for the Meobius functions of partially ordered sets, and we constructed a way to compute the Mobius function of any poset by a discrete sequential dynamical system (or viewed as an algorithm of inverting a triangular matrix in a way very different from the conventional algorithms).
11. Ricky Chen, On products of permutations with the most uncontaminated cycles by designated labels, Journal of Algebraic Combinatorics 57 (2023), pp. 1163-1171.
10. Ricky Chen, A versatile combinatorial approach of studying products of long cycles in symmetric groups, Advances in Applied Mathematics 133 (2022), 102283. (34 pages)
Highlights of the paper: (a) The work relates to a great deal of results on products of long cycles (E.g., G. Boccara, Discrete Math. (1980); R.P. Stanley, EuJC (2011); O. Bernardi et al., Combin. Probab. Comput. (2014); A. Hultman, Adv. in Appl. Math. (2014). ) (b) The first explicit formula tracking the number of cycles in $\alpha$-separated pairs; (That is, given a partition of a set, we obtain an explicit formula of the number of pairs of long cycles on the set such that the product of the long cycles does not mix the elements from distinct blocks of the partition and has an independently prescribed number of cycles for each block of elements.) (c) The first nontrivial explicit formula for strong separation probabilities; (Answering a call of R.P. Stanley for an explicit formula.) (d) New formulas enumerating the number of factorizations of a permutation into long cycles.
9. Ricky Chen, Combinatorially refine a Zagier-Stanley result on products of permutations, Discrete Mathematics 343(8) (2020), Article 111912. (5 pages)
8. Ricky Chen, A new bijection between RNA secondary structures and plane trees and its consequences, Electronic Journal of Combinatorics 26(4) (2019), P4. 48, 15 pages.
A beautiful relation: the joint distribution of the horizontal fiber decomposition and the vertical path decomposition of plane trees corresponds to the joint distribution of the odd level and even level degree distribution of their counterparts !
7. Ricky Chen, Signed relative derangements, reversal distance, and the signed Hultman numbers, Ars Combinatoria 147 (2019), pp. 281-288.
The study of signed relative derangements in this paper was motivated by computing the distribution of reversal distances of signed permutations, i.e., determining the so called signed Hultman numbers. We combinatorially proved that a subclass of signed relative derangements is enumerated by numbers satisfying a four-term recurrence. Next, we showed that these numbers give a natural upper bound for the number of signed permutations whose breakpoint graphs have only one alternating cycle. In fact, it was observed that a large portion of signed permutations are in this class.
6. Ricky Chen, Christian Reidys, A Combinatorial Identity Concerning Plane Colored Trees and its Applications , Journal of Integer Sequences, 20 (2017), Article 15.3.7, 9 pages.
The new identity can be used to prove a bijective problem of Richard Stanley (ranked 3), recover a new expression of the Narayana polynomials, and give an equivalent formula for the Harer-Zagier formula concerning moduli curves.
5. Ricky Chen, Christian Reidys, On the local genus distribution of graph embeddings, Journal of Combinatorial Mathematics and Combinatorial Computing, Vol. 101 (2017), pp. 157-173. [Note: The notion of local genus distribution was independently formulated around the same time by Gross et al. We posted our draft on arXiv in Mar. 2015 while their paper submission time was in Jan. 2015 as recorded in the journal EuJC and was not posted on arXiv.]
Given a graph embedding of genus g, using the plane permutation framework we study how locally reembedding a vertex affects the genus. As results, we have a local version of the interpolation theorem; we can compute the exact local minimum genus and maximum genus explicitly; we can compute the local genus polynomial which can be eventually shown to be always log-concave (while the global version is still an open conjecture); we obtain an easy-to-check necessary condition for an embedding to be an embedding of the minimum genus; finally, we have a simple lower bound for the probability of a ramdom embedding of a graph to be a one-face embedding (i.e., maximum genus embedding).
4. Ricky Chen, Christian Reidys, Plane permutations and applications to a result of Zagier-Stanley and distances of permutations, SIAM Journal on Discrete Mathematics 30(3) (2016), pp. 1660-1684.
Motivated by a new way of reading information sitting on one-face maps (unicellular maps or fatgraphs with one boundary component), we developed the theory of plane permutations. As results, we obtained several recurrences counting one-face hypermaps, or factorizations of a long cycle permutation, which refined and generalized Chapuy's recursion on unicellular maps; we gave another combinatorial proof of the Zagier-Stanley result on the number of facatorizations of a long cycle into a long cycle and a permutation with k cycles being counted by the so called Hultman numbers; and we presented one of the most simple, uniform frameworks studying transposition and block-interchange distances of permutations, as well as reversal distances of signed permutations together. For this last application to the genome rearrangement problems, we obtained a general lower bound, for which Bafna-Pevzner's lower bound and Chritie's formula based on cycle graphs are equivalent to evaluations at a special point. To some extent, we could come up with lots of different versions (n!) of cycle graphs, each giving us a lower bound and Bafna-Pevzner's cycle graph being one of them. So this framework may have extended this line of thinking to the most general case. In addition, by treating reversals as certain symmetric block-interchanges, we immediately obtained a new lower bound for the reversal distances of signed permutations. Some open problems were proposed too.
3. Ricky Chen, A Note on the Generating Function for the Stirling Numbers of the First Kind, Journal of Integer Sequences, Vol. 18 (2015), Article 15.3.8.
A more informative title maybe "A simple constructive proof for the generating function of the Stirling numbers of the first kind".
2. Ricky Chen, A refinement of the formula for k-ary trees and Gould-Vandermonde's convolution, Electronic Journal of Combinatorics 15(1)(2008), #R52, 9 pages.
The paper can be alternatively summarized as " A linear recurrence for generalized Catalan numbers and its applications". The linear recurrence for Catalan numbers has been referred to as Koshy's formula or Koshy's identity by George Andrews and others. Here the recurrence is proved by constructing an involution on k-ary trees. Riordan array theory is also utilized in the paper.
1. Ricky Chen, Louis Shapiro, On Sequences G_n Satisfying G_n=(d+2)G_{n-1}- G_{n-2} , Journal of Integer Sequences 10 (2007), Article 07.8.1, 10 pages.
A more suggestive title would be "Structures counted by certain Fibonacci-like sequences", as the sequence has the Fibonacci numbers as a special case when d = 1 with suitable initial conditions.
Ricky Chen, A brief introduction to Shannon's information theory, The Net Advance of Physics (MIT)--Information (2016), 14 pages. (received reads on my researchgate alone: 15,000+)
Can one break the Shannon capacity limit? We give a combinatorial exposition of Shannon's information theory. In particular, the Shannon entropy is obtained based on a simple counting argument (involving binomial coefficients) and the Stirling approximation formula. Surprisingly, to the best of our knowledge, similar description of this approach has been only employed by Edward Witten in "A Mini-Introduction to Information Theory". Some open discussion on whether Shannon's capacity limit can be broken or not is also presented.
2. Transmitting diversity (TxD) scheme enhancement for PUCCH format 3, 3GPP RAN1 #66, Athens, Greece, Aug. 22-26 (2011), R1-112462.
3. A/N coding schemes for large payload using DFT-S-OFDM, 3GPP RAN1 #62-bis, Xi'an, China, Oct. 11-15 (2010), R1-105247.
4. Evaluation of ACK/NACK transmission schemes for carrier aggregation, 3GPP RAN1 #61-bis, Dresden, Germany, June 28-July 2 (2010), R1-103884.
5. Feasibility and performance discussion on SR sharing, 3GPP RAN1 #60-bis, Beijing, China, Apr. 12-16 (2010), R1-101932.
Xiaofeng Chen, “New Insight into Communication---from theory to practice”, China Machine Press, Beijing, 2013.4 (now in its 4th reprint, has 2,000,000+ online reads so far). （In Chinese: 陈小锋，“通信新读-从原理到应用”，机械工业出版社，北京，2013.4）
M. Fu, et al., the Chinese translation of the book “Enumerative Combinatorics, vol. 1” by Richard P. Stanley, Higher Education Press, 2009.6. I translated some sections in Chapter 4 in the book.
I am the inventor or joint inventor (under the name Xiaofeng Chen) of more than 30 granted patents (in many places, e.g., USA (US), Europe (EP), China (CN), etc.) for 4G LTE/LTE-A and WiFi. Several of them have been adopted by Standards or products, for instance, the Dual Reed-Muller (RM) Coding family of patents used in 4G LTE/LTE-A.
Communication method, relay and communication system, CN101753198 B.
Method, apparatus and system for transmitting information bits, US8068548 B1. (Also granted in Europe, China, Korea, etc.)
Communication method for control channel and apparatus, US9553700 B2.
Method for detecting and sending control signaling, user equipment, and base station, US9148878 B2.
Method and apparatus for encoding and processing acknowledgement information, EP2654231 B1 (Granted in at least 5 countries/regions as well).
Communication method and apparatus, and receiving method and apparatus in wireless local area network, US9591650 B.
1. On a NEW lower bound for sorting signed permutations by reversals (with Andrei Bura, Christian Reidys), arXiv:1602.00778.
In our previous study of the reversal distance via plane permutations, we obtained a new lower bound. However, compared to the existing well-known Bafna-Pevzner bound through breakpoint graphs, it was not clear which one is better. In this paper, we showed that they are actually equal.
2. New formulas counting one-face maps and Chapuy's recursion (with Christian Reidys), arXiv:1510.05038
Walsh and Lehman obtained an explicit formula (with summation over certain partitions of the number g) for the number of one-face maps with n edges and genus g. Later, Harer and Zagier obtained the generating function for these numbers and a three-term recurrence (of both n and g), known as the Harer-Zagier formula and the Harer-Zagier recurrence, respectively. Very recently, Chapuy proved a new recurrence (of only g). We showed here that, starting with the Lehman-Walsh formula, we can derive new formulas which lead to the Harer-Zagier formula and recurrence as well as Chapuy's recurrence immediately.