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March 17, 2021 Limit shape of partitions via bijections Igor Pak, UCLA

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Page 1: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

March 17, 2021

Limit shape of partitions via bijections

Igor Pak, UCLA

Page 2: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 3: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 4: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 5: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 6: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 7: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 8: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

Limit shapes

Page 9: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

(P., 2004)

Page 10: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

(P., 2004)

Page 11: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

(P., 2004)

Page 12: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

Is Sylvester’s bijection a good bijection?

Page 13: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

Pak-Postnikov version of Sylvester’s bijection (1998)

Page 14: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 15: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

(Vershik, 1996)

Page 16: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

(Vershik, 1996)

Page 17: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 18: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 19: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

New results (some special cases)

Page 20: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

New results (some special cases)

Page 21: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 22: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent
Page 23: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

Limit shape of Lebesgue partitions

Page 24: Limit shape of partitions via bijectionspak/lectures/Slides/Part-talk... · 2021. 3. 17. · Let An denote the set of partitions of size n into distinct parts which are congruent

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SOME RESULTS IN PARTITIONS, PLANE PARTITIONS, AND ...sites.science.oregonstate.edu/~swisherh/LazarevMizuharaReid.pdfWe denote the plane partition function, PL(n), to be the number

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arxiv.org · arXiv:1707.02674v3 [math.NT] 1 Aug 2017 ON RANKS AND CRANKS OF PARTITIONS MODULO 4 AND 8 ERIC T. MORTENSON Abstract. Denote by p(n) the number of partitions of nand by

Congruent Communication

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CHAPTER 4- PART 2 Congruent Triangles. CPCTC (4-4) Definition of Congruent Triangles Corresponding Parts of Congruent Triangles are Congruent

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4-1 Congruent Figures - Wikispacesresources+KEY.pdf · Congruent polygons have congruent corresponding parts—their matching sides and angles. When you name congruent polygons, you

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Page 1 Page 2srochester.weebly.com/.../0/6/...congruent_figures.pdf · Congruent Figures EFGII Congruent Figures: Congruent polygons have congruent corresponding parts (matching sides

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 · Corresponding Parts of Congruent Triangles are Congruent e) Isosceles and Equilateral Triangles Two sides and angles are congruent All sides and angles are congruent. ... Proving

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Determine if the two shapes are congruent or not congruent. Write congruent if the two shapes are; and write not congruent if the shapes are

Some Results in Partitions, Plane Partitions, and ...math.oregonstate.edu/~swisherh/LazarevMizuharaReid.pdf · some results in partitions, plane partitions, and multipartitions oleg

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Congruent & Similar Polygons - · PDF fileCongruent Polygons Geometric figures are congruent that have the same size and shape. When figures are congruent, ... Congruent & Similar

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