Rishi Nath

activity

20092026

most citedPartitions with prescribed hooksets

20 citations · 31 across the 11 of their papers we have counts for

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9 papers · 1 filter

math.CO2025

On simultaneous $(s, s + t, s + 2 t, \dots)$ -core partitions

William Keith, Rishi Nath, James Sellers

We consider simultaneous $(s, s + t, s + 2 t, \dots, s + pt)$ -core partitions in the large- $p$ limit, or (when $s < t$ ), partitions in which no hook may be of length $s (mod t)$ . We study gene…

math.CO2019★ 2 cited

Cores and quotients of partitions through the Frobenius symbol

Olivier Brunat, Rishi Nath

The Frobenius symbol was first introduced in 1900 by Frobenius as a way to encode an integer partition. In 1941, motivated by the modular representation theory of the symmetric gro…

math.CO2019

Simultaneous core partitions with nontrivial common divisor

Jean-Baptiste Gramain, Rishi Nath, James A. Sellers

A tremendous amount of research has been done in the last two decades on $(s, t)$ -core partitions when $s$ and $t$ are positive integers with no common divisor. Here we change persp…

math.CO2016

Abaci structures of $(s, m s \pm 1)$ -core partitions

Rishi Nath, James A. Sellers

We develop a geometric approach to the study of $(s, m s - 1)$ -core and $(s, m s + 1)$ -core partitions through the associated $m s$ -abaci. This perspective yields new proofs for results of…

math.CO2015

A combinatorial proof of a relationship between maximal $(2 k - 1, 2 k + 1)$ and $(2 k - 1, 2 k, 2 k + 1)$ -cores

Rishi Nath, James A. Sellers

Integer partitions which are simultaneously $t$ --cores for distinct values of $t$ have attracted significant interest in recent years. When $s$ and $t$ are relatively prime, Olsson…

math.CO2014★ 1 cited

Symmetry in maximal $(s - 1, s + 1)$ cores

Rishi Nath

We explain a "curious symmetry" for maximal $(s - 1, s + 1)$ -core partitions first observed by T. Amdeberhan and E. Leven. Specifically, using the $s$ -abacus, we show such partitions ha…

On simultaneous (s,s+t,s+2t,…)-core partitions

Cores and quotients of partitions through the Frobenius symbol

Simultaneous core partitions with nontrivial common divisor

Abaci structures of (s,ms±1)-core partitions

A combinatorial proof of a relationship between maximal (2k−1,2k+1) and (2k−1,2k,2k+1)-cores

Symmetry in maximal (s−1,s+1) cores

On simultaneous $(s, s + t, s + 2 t, \dots)$ -core partitions

Abaci structures of $(s, m s \pm 1)$ -core partitions

A combinatorial proof of a relationship between maximal $(2 k - 1, 2 k + 1)$ and $(2 k - 1, 2 k, 2 k + 1)$ -cores

Symmetry in maximal $(s - 1, s + 1)$ cores