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arXiv · 2206.00131

Rectangular analogues of the square paths conjecture and the univariate Delta conjecture

Alessandro Iraci·Roberto Pagaria·Giovanni Paolini·Anna Vanden Wyngaerd
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Abstract

In this paper, we extend the rectangular side of the shuffle conjecture by stating a rectangular analogue of the square paths conjecture. In addition, we describe a set of combinatorial objects and one statistic that are a first step towards a rectangular extension of (the rise version of) the Delta conjecture, and of (the rise version of) the Delta square conjecture, corresponding to the case $q=1$ of an expected general statement. We also prove our new rectangular paths conjecture in the special case when the sides of the rectangle are coprime.

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Alessandro Iraci, Roberto Pagaria, Giovanni Paolini, Anna Vanden Wyngaerd. 2022-05-31. Rectangular analogues of the square paths conjecture and the univariate Delta conjecture. https://doi.org/10.5070/c63261980

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