BEGIN:VCALENDAR VERSION:2.0 PRODID:-//jEvents 2.0 for Joomla//EN CALSCALE:GREGORIAN METHOD:PUBLISH BEGIN:VTIMEZONE TZID:America/New_York BEGIN:STANDARD DTSTART:20241103T010000 RDATE:20250309T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20251102T010000 RDATE:20260308T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20261101T010000 RDATE:20270314T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20271107T010000 RDATE:20280312T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:STANDARD DTSTART:20281105T010000 RDATE:20290311T030000 TZOFFSETFROM:-0400 TZOFFSETTO:-0500 TZNAME:America/New_York EST END:STANDARD BEGIN:DAYLIGHT DTSTART:20240326T170000 RDATE:20241103T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20250309T030000 RDATE:20251102T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20260308T030000 RDATE:20261101T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20270314T030000 RDATE:20271107T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT BEGIN:DAYLIGHT DTSTART:20280312T030000 RDATE:20281105T010000 TZOFFSETFROM:-0500 TZOFFSETTO:-0400 TZNAME:America/New_York EDT END:DAYLIGHT END:VTIMEZONE BEGIN:VEVENT UID:ace04461e68b3e1f45b5cfe40b1541b8 CATEGORIES:Experimental Mathematics Seminar CREATED:20250319T132849 SUMMARY:Combinatorial exploration and permutation classes LOCATION:https://rutgers.zoom.us/j/94346444480 [password: The 20th Catalan number\, alias (40)!/(20!*21!) DESCRIPTION:Permutations, words, set partitions, and other such families of objects oft en play a role in diverse subfields of mathematics, physics and computer sc ience. When the structure of the object under investigation is known there are well-established tools, such as symbolic and analytic combinatorics, th at derive an enumeration, asymptotics, and the ability to randomly generate instances of the objects. However, the initial step from a definition of t he object to a structural description is often ad-hoc, human-staring-at-a-b lackboard type of work. This is the gap combinatorial exploration attempts to fill.\nCombinatorial exploration is a domain-agnostic algorithmic framew ork to automatically and rigorously study the structure of combinatorial ob jects and derive their counting sequences and generating functions. We desc ribe how it works and provide an open-source Python implementation. As a pr erequisite, we build up a new theoretical foundation for combinatorial deco mposition strategies and combinatorial specifications.\nCombinatorial explo ration has been most extensively applied to permutation classes, rederiving hundreds of results in the literature as well as discovering many novel re sults (which can be found on permpal.com). As well as unifying earlier meth ods, one key advantage of our approach is its ability to utilise a growing library of strategies in a simultaneous manner to build a greater understan ding of the structure of the permutation classes.\n X-ALT-DESC;FMTTYPE=text/html:

Permutations, words, set partitions, and other such famili es of objects often play a role in diverse subfields of mathematics, physic s and computer science. When the structure of the object under investigatio n is known there are well-established tools, such as symbolic and analytic combinatorics, that derive an enumeration, asymptotics, and the ability to randomly generate instances of the objects. However, the initial step from a definition of the object to a structural description is often ad-hoc, hum an-staring-at-a-blackboard type of work. This is the gap combinatorial expl oration attempts to fill.

Combinatorial exploration is a domain-agnostic algorithmic framework to automatically and rigorously stu dy the structure of combinatorial objects and derive their counting sequenc es and generating functions. We describe how it works and provide an open-s ource Python implementation. As a prerequisite, we build up a new theoretic al foundation for combinatorial decomposition strategies and combinatorial specifications.

Combinatorial exploration has been most extensively applied to permutation classes, rederiving hundreds of results in the literature as well as discovering many novel results (which can be found on permpal.com). As well as unifying earlier methods, one key advanta ge of our approach is its ability to utilise a growing library of strategie s in a simultaneous manner to build a greater understanding of the structur e of the permutation classes.

CONTACT: Christian Bean, Keele University DTSTAMP:20260826T211418 DTSTART;TZID=America/New_York:20250327T170000 DTEND;TZID=America/New_York:20250327T180000 SEQUENCE:0 TRANSP:OPAQUE END:VEVENT END:VCALENDAR