Dr. Nick Loehr · 2020. 3. 18. · Dr. Nick Loehr Associate Professor of Mathematics Virginia Tech...
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Marshall University Department of Mathematics Advanced Research Initiative Invited Speaker Dr. Nick Loehr Associate Professor of Mathematics Virginia Tech “Rook eory ” Monday, September 28, 2015 • Smith Hall 621 • 4:00pm Abstract Combinatorics is the mathematical theory of counting. In this talk, we introduce combinatorics through the subject of rook theory — which has nothing to do with chess! e rst goal of rook theory is to count congurations of rooks on general- ized chessboards so that no two rooks attack each other. e k ’th rook number of a board counts the number of such ways to place k rooks on the board. It oen happens that two dierent boards share the same rook numbers. is talk inves- tigates when and why this occurs by using geometric and algebraic manipulations of boards and rook placements. We present theorems of Foata/Schutzenberger and Goldman/Joichi/White characterizing rook-equivalent boards in various ways. e techniques used illustrate three branches of modern combinatorics — enumerative combinatorics, bijective combinatorics, and algebraic combinatorics. No prior knowl- edge of counting (or chess) is required for this talk. Department of Mathematics College of Science Marshall University 1 John Marshall Drive, Huntington WV 25755 (304) 696-6482
Transcript of Dr. Nick Loehr · 2020. 3. 18. · Dr. Nick Loehr Associate Professor of Mathematics Virginia Tech...
Marshall University Department of MathematicsAdvanced Research Initiative
Invited Speaker
Dr. Nick LoehrAssociate Professor of MathematicsVirginia Tech
“Rook�eory 101”Monday, September 28, 2015 • Smith Hall 621 • 4:00pm
Abstract
Combinatorics is the mathematical theory of counting. In this talk, we introducecombinatorics through the subject of rook theory — which has nothing to do withchess! �e �rst goal of rook theory is to count con�gurations of rooks on general-ized chessboards so that no two rooks attack each other. �e k’th rook number ofa board counts the number of such ways to place k rooks on the board. It o�enhappens that two di�erent boards share the same rook numbers. �is talk inves-tigates when and why this occurs by using geometric and algebraic manipulationsof boards and rook placements. We present theorems of Foata/Schutzenberger andGoldman/Joichi/White characterizing rook-equivalent boards in various ways. �etechniques used illustrate three branches of modern combinatorics — enumerativecombinatorics, bijective combinatorics, and algebraic combinatorics. No prior knowl-edge of counting (or chess) is required for this talk.
Department of Mathematics College of Science Marshall University1 John Marshall Drive, Huntington WV 25755 (304) 696-6482
