bibkey: mammez2022weakshuffle
authors: C. Mammez
year: 2022
title: "Weak stuffle algebras"
doi: 10.24330/ieja.1060709
url: https://arxiv.org/abs/2003.09142
claim: "Conjecture 3.10 asks whether Proposition 3.9 holds for every countable alphabet: over a field of characteristic 0, every weak shuffle product on the noncommutative polynomials is isomorphic, as an algebra, to the weak shuffle product with its exceptional off-diagonal coefficients normalized."
strata_touched:
  - D5/S1/Words/WeakShuffleNormalization
license: citation-only
triage: anchor

Mammez’s weak shuffle normalization conjecture

C. Mammez, Weak stuffle algebras, International Electronic Journal of Algebra 32 (2022), 1–45, DOI 10.24330/ieja.1060709, arXiv:2003.09142v3. Proposition 3.9 proves normalization for alphabets of cardinality two or three; Conjecture 3.10 asks whether the same normalization holds for every countable alphabet.

The formalization proves the normalization for every alphabet, including uncountable alphabets. The rescaling is diagonal on words: each exceptional ordered pair contributes the inverse coefficient to the exponent counting its admissible initial occurrences.

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DOI: https://doi.org/10.24330/ieja.1060709

Source: https://arxiv.org/abs/2003.09142