제목  OneDay Meeting in Combinatorics  

작성자  관리자  등록일  20190417  조회수  467 
OneDay Meeting in Combinatorics at AORC
Sergey Kitaev (Univ. of Strathclyde, UK) Title: Equidistributions on planar maps via involutions on description trees Date: 10:00  10:50, April. 8, 2019 (AORC Seminar Room) Abstract:
Description trees were introduced by Cori, Jacquard and Schaeffer in 1997 to give a general framework for the recursive decompositions of several families of planar maps studied by Tutte in a series of papers in the 1960s. We are interested in two classes of planar maps which can be thought of as connected planar graphs embedded in the plane or the sphere with a directed edge distinguished as the root. These classes are rooted nonseparable (or, 2connected) and bicubic planar maps, and the corresponding to them trees are called, respectively, β(1,0)trees and β(0,1)trees.
Sunmi Yun (Sungkyunkwan Universkty, Korea) Title: The Characteristic Polynomial of the Alternating Permutation Poset Date: 11:00  11:50, April. 8, 2019 (AORC Seminar Room) Abstract: For the symmetric group S_n, a permutation w can be considered as a word of simple transpositions s_i = (i, i+1). We define some order of permutations with respect to the minimal length of the word expression of each permutation. Then S_n with this order is a poset. We consider the set of alternating permutations with the same order, which is also a poset. We call it the alternating permutation poset. It turns out that its characteristic polynomial has a nice form. In this talk we prove this property.
Travis Scrimshaw(Univ. of Queensland, Australia) Title: Stump's q,tCatalan numbers, representation theory, and beyond Date: 14:00  14:50, April. 8, 2019 (AORC Seminar Room) Abstract: The Catalan numbers form one of the most famous sequences in combintorics and are counted by over 200 objects. By summing over such an object, say Dyck paths, with a statistic such as major index, we construct a qanalog of the Catalan numbers. By further refining major index, Christian Stump introduced a q,tanalog of the Catalan numbers and has a natural specialization to the (Mahonian) qCatalan numbers. In this talk, we will give an interpretation of Stump's q,tCatalan numbers as a form of the character of a particular representation of the type C Lie algebra. As a consequence, the principal specialization of the character is the qCatalan number. Then, by extending our approach to the entire rectangular lattice, we show that we obtain the qbinomal coefficients. This is joint work with Sejin Oh.
Stephanie van Willigenburg (UBC, Canada) Title: The epositivity of chromatic symmetric functions Date: 15:00  15:50, April. 8, 2019 (AORC Seminar Room) Abstract:
The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, epositivity.
Brendon Rhoades (UCSD, USA) Title: Spanning configurations Date: 16:30  17:20, April. 8, 2019 (AORC Seminar Room) Abstract: A finite sequence (W1,W2,...,Wr) of subspaces of the complex vector space C^k is a spanning configuration if W1 + W2 + · · · + Wr = C^k . We present the cohomology of the moduli space of spanning configurations where the sequence of dimensions dim(W1),dim(W2),...,dim(Wr) is fixed. We explain connections to combinatorics and, in particular, symmetric function theory. Joint with Brendan Pawlowski and Andy Wilson.

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