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Partial symmetries of iterated plethysms | | Álvaro Gutiérrez
; Mercedes H. Rosas
; | | Date: |
1 Jan 2022 | | Abstract: | We study the coefficients of the Schur expansion of iterated plethysms,
$s_{lambda_1}øs_{lambda_2}øcdots s_{lambda_k} = sum a_mu s_mu$. For
certain choices of $lambda_1$, ..., $lambda_k$, these coefficients express
partial symmetries. We formalize this symmetry by means of an involution on
partitions, and show that if $f$ has this symmetry, then $s_lambdaøf$ too
for $lambdainmathtt{Par}(2)$.
We give explicit formulas for the plethysms $s_2øs_bøs_a$ and $s_cø
s_2øs_a$, $a,b,cinN_{ge2}$ and show that they have this partial symmetry.
Finally, we make some remarks and conjectures regarding unimodality and
asymptotic normality of the coefficients involved. | | Source: | arXiv, 2201.00240 | | Services: | Forum | Review | PDF | Favorites | |
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