 August 7 (Wednesday)
 13h30  00h00 Registration
 14h20  14h30 Opening Ceremony
 14h30  18h00 Session 7A
 14h30  15h30 7A1 Keynote Lecture I (View, Download)
 Speaker Richard P. Stanley, MIT, USA
 Title Two enumerative tidbits
 Abstract We discuss two unrelated results in enumerative combinatorics.
 (i) Smith normal form of a matrix related to Young diagrams. We generalize a result of Carlitz, Roselle, and Scoville on a combinatorial matrix of determinant one by introducing additional parameters and computing the Smith normal form of the resulting matrix.
 (ii) A distributive lattice associated with threeterm arithmetic progressions (with Fu Liu). We prove two conjectures of Noam Elkies related to arithmetic progressions of length three by showing a connection with a distributive lattice of certain semistandard Young tableaux.
 15h45  16h45 7A2 Talk I
 Speaker Richard A. Askey, University of WisconsinMadison, USA
 Title The magical connection between balanced and wellpoised series, both hypergeometric and basic hypergeometric
 Abstract Hypergeometric series with the qbinomial theorem. There are two natural first steps one can take.
(1x)^{a}(1x)^{b} = (1x)^{a+b}
(1x)^{a}(1+x)^{a} = (1x^{2})^{a}
When the binomial theorem is used on each series and the coefficients of x^{n} are equated, the first identity is an instance of what will become balanced series when more parameters are introduced, and the second is an instance of wellpoised series, and later very wellpoised series. At this stage the two identities have nothing to do with each other. At a higher level the two chains of identities become related, Whipple's formula for hypergeometric series and Watson's extension for basic hypergeometric series. Other connections will be mentioned, and two different extensions beyond this level will be described. One, which is due to George Andrews, contains variants of the RogersRamanujan identities. The other has a mysterious twist which I do not understand.
 17h00  18h00 7A3 Talk II (View, Download)
 Speaker Sangwook Kim, Chonnam National University, Korea
 Title Enumeration of Schröder families by type
 Abstract Schröder paths, sparse noncrossing partitions, and partial horizontal strips are three classes of Schröder objects which carry a notion of type. We provide typepreserving bijections among these objects and an explicit formula which enumerates these objects according to type and length. We also define a notion of connectivity for these objects and discuss an analogous formula which counts connected objects by type. This is joint work with Suhyung An and SenPeng Eu.
 August 8 (Thursday)
 10h00  12h30 Session 8A
 10h00  11h00 8A1 Talk III (View, Download)
 Speaker Mitsugu Hirasaka, Pusan National University, Korea
 Title Zeta functions of adjacency algebras induced by graphs
 Abstract Let Γ denote a finite digraph and R_{Γ} denote the subring generated by the adjacecny matrix of Γ In this talk we focus on the number a_{n} of ideals of R_{Γ} with index n, and show a way to find the formal Dirichlet series
Σ_{n≥1} a_{n} n^{s}
when Γ can be a relation of an association scheme of prime order. This is a joint work with Akihide Hanaki.
 11h30  12h30 8A2 Talk IV (View, Download)
 Speaker Jiang Zeng, Université Claude Bernard Lyon 1, France
 Title JacobiStirling numbers and JacobiStirling permutations
 Abstract The JacobiStirling numbers were discovered as a result of a problem involving the spectral theory of powers of the classical second order Jacobi differential expression. They are refinements of the LegendreStirling numbers and generalize the Stirling numbers and central factorial numbers. In this talk I will report on the recent work about the combinatorics of these numbers. Moreover, the diagonal generating functions of JacobiStirling numbers are rational functions, of which the numerators are the enumerative polynomials of the JacobiStirling permutations.
 12h30  12h40 Group Photo
 12h40  14h30 Lunch
 14h30  18h00 Session 8B
 14h30  15h30 8B1 Keynote Lecture II (View, Download)
 Speaker Richard P. Stanley, MIT, USA
 Title Polynomial sequences of binomial type
 Abstract A sequence p_{0}(n), p_{1}(n), ... of complex polynomials is of binomial type if p_{0}(n)=1 and
Σ_{k≥0} p_{k}(n) x^{k }/ k! = ( Σ_{k≥0} p_{k}(1) x^{k }/ k! )^{n}.
Such polynomials play a fundamental role in the theory of operator calculus developed by G.C. Rota and his collaborators. After briefly reviewing this theory, we will focus on examples of such polynomials. In particular, we discuss recent work of J. Schneider related to placing figures on tori. An application is given to chromatic polynomials of toroidal grid graphs.
 15h45  16h45 8B2 Talk V (View, Download)
 Speaker Mourad E. H. Ismail, University of Central Florida, USA
 Title Combinatorics of 2DHermite polynomials
 Abstract We discuss the combinatorics and generating functions of the 2DHermite polynomials. This is partly based on joint work with Plamen Simeonov.
 17h00  18h00 8B3 Talk VI (View, Download)
 Speaker Suyoung Choi, Ajou University, Korea
 Title Introduction to the anumber of graphs and hypergraphs
 Abstract Recently, I and my colleague Park have introduced new combinatorial invariants, called the anumber, of any finite simple graph, which arise in toric topology. Interestingly, for specific families of the graph, our invariants are deeply related to wellknown combinatorial sequences such as the Catalan numbers and Euler zigzag numbers. In this talk, I introduce several further works on this topic, and I will discuss about the analogue of the invariant for hypergraphs.
 18h00  21h00 Banquet
 August 9 (Friday)
 10h00  12h30 Session 9A
 10h00  11h00 9A1 Talk VII (View, Download)
 Speaker Soojin Cho, Ajou University, Korea
 Title LittlewoodRichardson numbers of Schur's S and PFunctions
 Abstract LittlewoodRichardson numbers(LRnumbers) are structure constants of Schur's Sfunctions. Many combinatorial models for LRnumbers of Schur functions are known and they are very well understood. We review known combinatorial rules to calculate LRnumbers and interesting properties of LRnumbers including symmetries and factorization theorem. We then introduce eight useful reduction formulae deleting one or two rows (columns) of each partition. As an application, we prove that if the LRnumber is 1 and each partition has distinct parts, then one of two types of our reduction formulae is always applicable and hence we have an algorithm to test if the LRnumber is 1.
 There do not exist so many combinatorial models of LRnumbers for Schur's Pfunctions. We introduce a new LRrule for Schur's Pfunctions and some properties of them.
 11h30  12h30 9A2 Talk VIII (View, Download)
 Speaker SenPeng Eu, National University of Kaohsiung, Taiwan
 Title Signed Counting of Euler numbers
 Abstract Euler numbers count several important classes of permutations, among them the alternating permutations and the simsun permutations. In this talk we introduce some new results on the signed counting of these permutations.
 12h30  14h30 Lunch
 14h30  18h00 Session 9B
 14h30  15h30 9B1 Keynote Lecture III (View, Download)
 Speaker Richard P. Stanley, MIT, USA
 Title Valid orderings of hyperplane arrangements
 Abstract Let A be a finite set of hyperplanes in R^{n}. Let L be a sufficiently generic directed line in R^{n} Then L intersects the hyperplanes in A in a certain order, called a valid ordering of A. We will discuss connections between valid orderings and such topics as line shellings of polytopes, the Dilworth truncation of a matroid, and a generalization of chromatic polynomials. Some knowledge of matroid theory will be useful but not essential for understanding this lecture.
 15h45  16h45 9B2 Talk IX (View, Download)
 Speaker Dennis Stanton, University of Minnesota, USA
 Title Reflection factorizations of Singer cycles
 Abstract The number of factorizations of an ncycle in S_{n} into n1 transpositions is n^{n2}. We consider a version of this theorem when GL_{n}(F_{q}) replaces S_{n}, the Singer cycle replaces an ncycle, and reflections replace transpositions. We give explicit enumeration formulas for this question, and also longer factorizations. The answers involve a mixture of binomial and qbinomial coefficients. Character techniques are used, no bijective proofs are known. This is joint work with Joel Lewis and Vic Reiner.
 17h00  18h00 9B3 Talk X (View, Download)
 Speaker Jang Soo Kim, KIAS, Korea
 Title Moments of AskeyWilson polynomials
 Abstract The AskeyWilson polynomials are the most general orthogonal polynomials among those classified by the Askey scheme. These are orthogonal polynomials in one variable with 5 parameters. In this talk I will talk about 3 combinatorial methods to study the nth moment of the AskeyWilson polynomials. The first method is Viennot's theory of weighted Motzkin paths. The second method uses staircase tableaux introduced by Corteel and Williams. The third method is a modification of an idea of Ismail, Stanton, and Viennot on matchings and qHermite polynomials. Using the third method we express the nth moment as a fraction of two generating functions for certain matchings and obtain a new formula for the moment. This is joint work with Dennis Stanton.
 18h00  00h00 Closing Ceremony

