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nLab > Latest Changes: shuffle

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  1.  

  1. added an older reference

    diff, v20, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeJul 10th 2021

    added pointer to:

    diff, v21, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2022

    I have tried to streamline this entry, for instance in moving the remark on “unshuffles” out of a superfluous subsection and right into the Idea-section, and in collecting all variants of stating the definition right there in the Definition-section.

    diff, v22, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2022
    • (edited Dec 4th 2022)

    added an illustration (here)

    also edited and expanded the wording in the Idea-section

    diff, v22, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeDec 4th 2022
    • (edited Dec 4th 2022)

    I have created a “Properties”-section (now here) and added to it two subsections that used to be at product of simplices (but don’t say anything directly about simplices):

    “The poset of (p,q)(p,q)-shuffles” and “The Anti-Lex order”.

    Both these sections leave room for streamlining. Also, their graphics remains broken, and have been for a long time (already when we discussed this last time here)

    diff, v23, current

  6. Replaced broken presheaf.com diagrams with xypic. Images recovered from https://web.archive.org/web/20221002041758/https://ncatlab.org/nlab/show/product+of+simplices

    Jon Rowlands

    diff, v24, current

    • CommentRowNumber7.
    • CommentAuthorUrs
    • CommentTimeNov 7th 2023
    • (edited Nov 7th 2023)

    added the remark (here) that the number of (p,q)(p,q)-shuffles is given by the binomial coefficient for choosing pp out of p+qp+q elements.

    What I am really after: The signed sum of (p,q)(p,q)-shuffles

    ∑sh∈Sh(p,q)sgn(sh) \underset{ \mathclap{ sh \in Sh(p,q) } }{\sum} \; sgn(sh)

    as a function ℕ×ℕ→{0,1}\mathbb{N} \times \mathbb{N} \to \{0,1\}. (?)

    diff, v25, current

    • CommentRowNumber8.
    • CommentAuthorTim_Porter
    • CommentTimeNov 7th 2023

    Fixed a typo

    diff, v26, current

1 to 8 of 8

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