DSpace Community: KAIST Dept. of Mathematical Sciences
http://hdl.handle.net/10203/527
KAIST Dept. of Mathematical Sciences2018-02-18T00:01:17ZA sextuple equidistribution arising in Pattern Avoidance
http://hdl.handle.net/10203/237661
Title: A sextuple equidistribution arising in Pattern Avoidance
Authors: Lin, Zhicong; Kim, Dongsu
Abstract: We construct an intriguing bijection between 021-avoiding inversion sequences and (2413,4213)-avoiding permutations, which proves a sextuple equidistribution involving double Eulerian statistics. Two interesting applications of this result are also presented. Moreover, this result inspires us to characterize all permutation classes that avoid two patterns of length 4 whose descent polynomial equals that of separable permutations.2018-04-01T00:00:00ZRank gain of Jacobian varieties over finite Galois extensions
http://hdl.handle.net/10203/237144
Title: Rank gain of Jacobian varieties over finite Galois extensions
Authors: Im, Bo-Hae; Wallace, Erik
Abstract: Let K be a number field, and let X -> P-K(1) be a degree p covering branched only at 0, 1, and infinity. If K is a field containing a primitive p-th root of unity then the covering of P-1 is Galois over K, and if p is congruent to 1 mod 6, then there is an automorphism sigma of X which cyclically permutes the branch points. Under these assumptions, we show that the Jacobian of both X and X/<sigma > gain rank over infinitely many linearly disjoint cyclic degree p-extensions of K. We also show the existence of an infinite family of elliptic curves whose j-invariants are parametrized by a modular function on Gamma(0)(3) and that gain rank over infinitely many cyclic degree 3-extensions of Q.2018-03-01T00:00:00ZPartitioning H-minor free graphs into three subgraphs with no large components
http://hdl.handle.net/10203/211874
Title: Partitioning H-minor free graphs into three subgraphs with no large components
Authors: Liu, Chunhung; Oum, Sang-il
Abstract: We prove that for every graph H, if a graph G has no H minor, then V(G) can be partitioned into three sets such that the subgraph induced on each set has no component of size larger than a function of H and the maximum degree of G. This answers a question of Esperet and Joret and improves a result of Alon, Ding, Oporowski and Vertigan and a result of Esperet and Joret. As a corollary, for every positive integer t, if a graph G has no Kt+1 minor, then V(G) can be partitioned into 3t sets such that the subgraph induced on each set has no component of size larger than a function of t. This corollary improves a result of Wood.2018-01-01T00:00:00ZExceptional collections on Dolgachev surfaces associated with degenerations
http://hdl.handle.net/10203/239451
Title: Exceptional collections on Dolgachev surfaces associated with degenerations
Authors: Cho, Yonghwa; Lee, Yongnam
Abstract: Dolgachev surfaces are simply connected minimal elliptic surfaces with p(g) = q = 0 and of Kodaira dimension 1. These surfaces are constructed by logarithmic transformations of rational elliptic surfaces. In this paper, we explain the construction of Dolgachev surfaces via Q-Gorenstein smoothing of singular rational surfaces with two cyclic quotient singularities. This construction is based on the paper [25]. Also, some exceptional bundles on Dolgachev surfaces associated with Q-Gorenstein smoothing have been constructed based on the idea of Hacking [12]. In the case if Dolgachev surfaces were of type (2,3), we describe the Picard group and present an exceptional collection of maximal length. Finally, we prove that the presented exceptional collection is not full, hence there exists a nontrivial phantom category in the derived category. (C) 2017 Elsevier Inc. All rights reserved.2018-01-01T00:00:00Z