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History of the Lattice Path Conference

"Reminiscing over: a short historical view on the series of conferences", by its founder Sri Gopal Mohanty

[This text is based on the text written by Gopal for the Siena conference in 2010, a version of which was published in Fundamenta Informaticae 117 (2012). For this web version, it was slightly modified/updated with photos and links added.]

The two first books dedicaded to lattice paths,
by Narayana and Mohanty in 1979.
Just after almost simultaneous publications in 1979 of two books, “Lattice Path Combinatorics with Statistical Applications”, by Tadepalli Venkata Narayana and “Lattice Path Counting and Applications”, by me, I realized that there was a substantial growing interest in lattice path combinatorics, with applications in computer science, statistics and applied probability. I also realized that the distribution of researchers was world wide. In order to increase the awareness of the subject, my intention to organize a conference to bring eminent and young researchers together and to promote interaction between the theory group and those involved in applications resulted in the first Conference on Lattice Path Combinatorics and Applications that was held at McMaster University, Canada in 1984. Incidentally, I have been at McMaster University since 1964 and the University was highly supportive of my initiative to organize the conference. Its success prompted quite a few to voice an encore for it. In the mean time the publication of two books, “Combinatorial Enumeration” by Ian Goulden and David Jackson in 1983 and “Enumerative Combinatorics - Vol 1” by Richard Stanley in 1986 encouraged me to organize another conference.
Lattice Path'1990, McMaster

B. L. S. Prakasa Rao, Endre Csáki,
István Vincze, Gopal Mohanty
at the Lattice Path Conference,
in 1994 at Delhi.

Lattice Path'1994, Delhi
Lattice Path'1998, Wien
The second conference was held again at McMaster University in 1990, although some of the enthusiasts wished it to be held earlier. Both conferences had international participation and triggered so much interest that participants showed their willingness to organize next events. Thus, subsequent conferences were called International and were held at University of Delhi in 1994, University of Vienna in 1998, University of Athens in 2002 and East Tennessee State University in 2007, University of Siena in 2010, Cal Poly Pomona university in 2015. The main local organizers of these events were Kanwar Sen in India, Walter Böhm and Christian Krattenthaler in Austria, Charalambos A. Charalambides in Greece, Anant Godbole in USA, Renzo Pinzani and Simone Rinaldi in Italy, Alan Krinik in USA in 2015. The international nature is also reflected by regular participations from Australia, Austria, Bangladesh, Canada, China, France, Germany, Greece, India, Italy, Japan, Kazakhstan, South Korea, South Africa, Sweden, Taiwan, UK, and USA.
Lattice Path'2007, Johnson City
Lattice Path'2010, Siena

Henri Delannoy (1833 - 1915) [above], William Allen Whitworth (1840 - 1905), and Désiré André (1850 - 1917), fathers of lattice path theory (with publications resp. in 1886, 1878, 1887, motivated by the "ruin problem" and the "ballot problem" of Pascal, de Moivre, Laplace, Bertrand, etc.)  
Germain Kreweras (1918 - 1998),
one of the seminal contributors to lattice path theory. He is, with Louis Comtet, Dominique Foata, and Marcel-Paul Schützenberger, the father of modern enumerative
combinatorics in France.

Throughout the years, the topics covered ranges over wide but related varieties like lattice path and other combinatorial problems, q-calculus, orthogonal polynomials, plane partitions, Stirling numbers, hypergeometric functions, partial orders, spanning surfaces, generating functions, recurrence relations, bijectivity, algebraic geometry, asymptotics, random walks, nonparametric inference, discrete distributions, urn models, queueing theory, quality control and other fields of applications such as probability, statistics, physics, psychology, management science and computer science. In Greece Conference, the title changed to Lattice Path Combinatorics and Discrete Distributions in order to emphasize the “Discrete Distributions” content.
A new initiative started by dedicating the Fourth Conference at Wien to the memory of Germain Kreweras (1918 - 1998) and Tadepalli Venkata Narayana (1930 - 1987), both of whom made a significant contribution to the field. In the same spirit, the 2002 conference was dedicated to the memory of István Vincze (1912 - 1999). The 2015 conference was dedicated to Shreeram Shankar Abhyankar (1930 - 2013), Philippe Flajolet (1948 - 2011), and Lajos Takács (1924 - 2015).
The number of participants was remarkably steady to be 60 - 70. It allowed us a format of conference alloting around 25 minutes to each paper. They were also instructional lectures of longer duration, reviewing topics of current interest. The conferences were typically of two and a half day duration and the organizers have so far been able to arrange some entertainment programmes and sometimes after-dinner speakers. Let us for example here mention the "Mathemagics" show of our colleague Arthur Benjamin at the 2015 conference at Pomona, or the Catalan vs Fibonacci football match at Siena!
Philippe Flajolet (1948 - 2011)
developed analytic methods in enumerative and asymptotic combinatorics, and worked on links between lattice paths and continued fractions, with applications to computer science, statistical mechanics...
Lajos Takács (1924 - 2015)
did numerous contributions to lattice path theory, in link with queueing theory and Brownian motion, similarly to other great probabilists like William Feller or Sparre Andersen.

Will you participate in
the next special issue? :-)

The refereed papers among those presented at each conference were published in special issues of the Journal of Statistical Planning and Inference (for this process, we had the pleasure to interact with the founding editor of this journal, Jagdish Srivastava, from Elsevier Publication, and when he passed away, we switched to Fundamenta Informaticae for the 2010 conference and then to the Springer's "Developments in Mathematics" for the 2015 conference). We are pleased that the special issue related to the 2021 conference will be in free access, published by the Séminaire Lotharingien de Combinatoire.

In the journey over so many years, quite a few have decided to walk all along by my side. They are more than colleagues, they are indeed true friends. I also thank others who have decided to join with us supplying food and water to the walkers through their participation and organizational help. The humble beginning and the smallness of the Lattice Path Conferences have provided a close affinity among those who have been participating: They have become members of what I call “Lattice Path” family. I wish a successful future journey and the well-being of the family!

Two types of "lattice" paths; the last one is by Claude Monet...

List of lattice path conferences and related events: