Promotion and rowmotion
نویسندگان
چکیده
منابع مشابه
Promotion and rowmotion
We present an equivariant bijection between two actions—promotion and rowmotion—on order ideals in certain posets. This bijection simultaneously generalizes a result of R. Stanley concerning promotion on the linear extensions of two disjoint chains and certain cases of recent work of D. Armstrong, C. Stump, and H. Thomas on noncrossing and nonnesting partitions. We apply this bijection to sever...
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Various authors have studied a natural operation (under various names) on the order ideals (equivalently antichains) of a finite poset, here called rowmotion. For certain posets of interest, the order of this map is much smaller than one would naively expect, and the orbits exhibit unexpected properties. In very recent work (inspired by discussions with Berenstein) Einstein and Propp describe h...
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We study a birational map associated to any finite poset P . This map is a farreaching generalization (found by Einstein and Propp) of classical rowmotion, which is a certain permutation of the set of order ideals of P . Classical rowmotion has been studied by various authors (Fon-der-Flaass, Cameron, Brouwer, Schrijver, Striker, Williams and many more) under different guises (Striker-Williams ...
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Birational rowmotion – a birational map associated to any finite poset P – has been introduced by Einstein and Propp as a far-reaching generalization of the (wellstudied) classical rowmotion map on the set of order ideals of P . Continuing our exploration of this birational rowmotion, we prove that it has order p+q on the (p, q)rectangle poset (i.e., on the product of a p-element chain with a q...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2012
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2012.05.003