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講演会
過去の記録 ～06/25｜次回の予定｜今後の予定 06/26～
2012年07月23日(月)
16:30-17:30 数理科学研究科棟(駒場) 126号室
Thomas W. Roby 氏 (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
Thomas W. Roby 氏 (University of Connecticut)
Combinatorial Ergodicity (ENGLISH)
[ 講演概要 ]
Many cyclic actions tau on a finite set S of
combinatorial objects, along with many natural
statistics phi on S, exhibit``combinatorial ergodicity'':
the average of phi over each tau-orbit in S is
the same as the average of phi over the whole set S.
One example is the case where S is the set of
length n binary strings a1dotsan
with exactly k 1's,
tau is the map that cyclically rotates them,
and phi is the number of \\textit{inversions}
(i.e, pairs (ai,aj)=(1,0) for iJ less than j).
This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.
This is joint work with Jim Propp.
Many cyclic actions tau on a finite set S of
combinatorial objects, along with many natural
statistics phi on S, exhibit``combinatorial ergodicity'':
the average of phi over each tau-orbit in S is
the same as the average of phi over the whole set S.
One example is the case where S is the set of
length n binary strings a1dotsan
with exactly k 1's,
tau is the map that cyclically rotates them,
and phi is the number of \\textit{inversions}
(i.e, pairs (ai,aj)=(1,0) for iJ less than j).
This phenomenon was first noticed by Panyushev
in 2007 in the context of antichains in root posets;
Armstrong, Stump, and Thomas proved his
conjecture in 2011.
We describe a theoretical framework for results of this kind,
and discuss old and new results for products of two chains.
This is joint work with Jim Propp.
