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

该奖项将为将于2014年7月7日至11日在东田纳西州立大学举行的“置换模式2014”(http://www.etsu.edu/cas/math/pp2014)，)会议提供资金。排列模式是一个在过去二十年里已经成为组合学的一个成熟分支的主题。该领域的大部分研究都集中在避免的排列类别上，即这样一个类别中的每个排列都避免了特定的子序列集。事实证明，模式避免在理论计算机科学中自然而然地出现，以表征许多自然排序设备的可能输出集，例如堆栈；事实上，Knuth的结果是单栈可排序的，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。当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，吸引了一批枚举学、分析学、代数和概率组合学的研究人员，他们都对围绕排列或词语的模式避免或遏制的研究问题有共同的兴趣。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大会使命的重要组成部分。来自PI的本科生暑期研究体验项目的八名学生将参加2014年的会议，过去该项目的参与者也可能参加。奖励基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.