Combinatorics of the Diagonal Harmonics

Hicks, Angela

doi:10.1007/978-3-030-05141-9_5

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By Equation (31) We See That If1

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2019

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“…The shuffle conjecture is a combinatorial formula for computing DH n [Z; q, t] in Equation (3.2), but before we give it and do an example we will briefly recount a skeletal history of what motivated it. More details on this fascinating story can be found in the excellent state-of-the-art survey article by Hicks [21], and the illuminating texts by Bergeron [3] and Haglund [14].…”

Section: By Equation (31) We See That Ifmentioning

confidence: 99%

The shuffle conjecture

Willigenburg

2019

Bull. Amer. Math. Soc.

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Walks in the plane taking unit-length steps north and east from (0, 0) to (n, n) never dropping below y = x and parking cars subject to preferences are two intriguing ingredients in a formula conjectured in 2005, now famously known as the shuffle conjecture.Here we describe the combinatorial tools needed to state the conjecture. We also give key parts and people in its history, including its eventual algebraic solution by Carlsson and Mellit, which was published in the Journal of the American Mathematical Society in 2018. Finally, we conclude with some remaining open problems.

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Section: By Equation (31) We See That Ifmentioning

confidence: 99%

The shuffle conjecture

Willigenburg

2019

Bull. Amer. Math. Soc.

View full text Add to dashboard Cite

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Combinatorics of the Diagonal Harmonics

Cited by 1 publication

References 46 publications

The shuffle conjecture

The shuffle conjecture

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