Conferences in the Mathematical Sciences -- Permutation Patterns 2014, July 7-11, 2014

该奖项为“排列模式2014”会议（http://www.etsu.edu/cas/math/pp2014）提供资金支持，该会议将于2014年7月7日至11日在东田纳西州立大学举行。在过去的二十年里，排列模式已经成为组合学的一个分支。该领域的大部分研究都集中在避免排列的类别上，即此类中的每个排列都会避免某些子序列集。事实证明，模式避免在理论计算机科学中自然出现，以表征许多自然排序设备（如堆栈）的可能输出集；事实上，Knuth的结果，即列表是一层可排序的，当且仅当它避免了模式231，被认为是丰富的排列模式理论的基石之一。目前的新研究涉及复杂性理论和理论计算机科学等领域。自2003年以来，“排列模式”系列会议每年举行一次，吸引了枚举学、解析学、代数学和概率组合学领域的研究人员，他们都对围绕排列或单词中的模式避免或遏制的研究问题感兴趣。多年来，参加这次会议的女性、本科生和研究生以及早期职业教师的数量稳步增加。事实上，培养和指导这样的数学家一直是会议使命的重要组成部分。来自PI本科生暑期研究经历项目的8名学生将参加2014年的会议，该项目过去的参与者也将参加。奖励资金专门用于支持美国公民和永久居民的参与。

This award is providing funds to support the conference "Permutation Patterns 2014" (http://www.etsu.edu/cas/math/pp2014), which will be held July 7-11, 2014 at East Tennessee State University. Permutation Patterns is a subject that has become an established branch of Combinatorics over the last two decades. Much of the research in the area has centered on classes of permutations that are avoiding, i.e., each permutation in such a class avoids certain sets of subsequences. It turns out that pattern avoidance arises naturally in theoretical computer science to characterize the set of possible outputs of many natural sorting devices, such as stacks; in fact Knuth's result that a list is one-stack sortable if and only it avoids the pattern 231 is considered to be one of the cornerstones of the rich theory of permutation patterns. Current new research involves areas such as complexity theory and theoretical computer science. The conference series "Permutation Patterns" has been held annually since 2003, and has attracted a community of researchers in enumerative, analytic, algebraic and probabilistic combinatorics, all with common interest in research questions that revolve around pattern avoidance or containment in permutations or words.The numbers of women, undergraduate and graduate students, and early career faculty who attend this conference have increased steadily over the years. Indeed, nurturing and mentoring of such mathematicians has been a significant part of the conference mission. Eight students from the PI's summer Research Experiences for Undergraduates program will attend the conference in 2014, as might past participants from the program. Award funds are dedicated to supporting participation of US citizens and permanent residents.