組合數學新苗研討會

邀請演講

講者：林延輯 

單位/職稱：國立台灣師範大學數學系 副教授

講題：Equiangular lines 

大綱：Lines through the origin in Euclidean spaces are called equiangular if every pair of those lines intersect with each other at the same angle. The maximum cardinality of such a line system in R^n has been studied since 1948. In this talk we will focus on the methods obtaining bounds of these cardinalities. The upper bounds came from algebraic graph theory and linear programming, while the lower bounds arose from various constructions such as Steiner triple systems, lattices, and combinatorial designs. 

講者：蔡昇甫 

單位/職稱：國立中央大學數學系助理教授 

講題：Extremal bounds for pattern avoidance in 0-1 matrices

大綱：A 0-1 matrix M contains another 0-1 matrix P if M has a submatrix that can be transformed to P by flipping any number of 1s to 0s. Otherwise M avoids P. M is P-saturated if it avoids P and flipping any of its 0 makes it contain P. Extremal functions ex(n,P) and sat(n,P) are the maximum and minimum possible number of 1s in a n-by-n 0-1 matrix that is P-saturated, respectively. In this talk, we will review this research area, including the overview, its connection with classical extremal problem for graphs, developed techniques, and our findings over the years.

講者：葉均承 

單位/職稱：高雄師範大學數學系 副教授 

講題：Eulerian pairs and Eulerian recurrence systems 

大綱：In this talk, I will introduce the definitions of Eulerian pair and Hermite-Biehler pair, and also characterize a duality relation between Eulerian recurrences and Eulerian recurrence systems. This generalizes and unifies Hermite-Biehler decompositions of several enumerative polynomials, including up-down run polynomials for symmetric groups, alternating run polynomials for hyperoctahedral groups, flag descent polynomials for hyperoctahedral groups and flag ascent-plateau polynomials for Stirling permutations. These derive some properties of associated polynomials. In particular, proveing the alternatingly increasing property and the interlacing property of the ascent-plateau and left ascent-plateau polynomials for Stirling permutations.   

重要日期

• 2023 年 7 月16 日（日）：報名演講、優秀論文獎、種苗報告截止日期

• 2023 年 7 月 30 日（日）：線上註冊截止日期

• 2023 年 8 月 28 – 29 日（一、二）：組合數學新苗研討會

優秀論文徵求

承襲以往研討會之作法，藉由公正且專業的論文審查小組，從與會之碩博士畢業生論文中挑選優秀論文，並於會議之閉幕典禮上頒獎。