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数学

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Andrius Kulikauskas

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See: Combinatorics

Organize the interpretations of various combinatorial objects


  • How does the expansion (x1 + ... + xm)N relate to the matrix of nonnegative integers? and how it yields pairs of Kostka matrices? (form and content)?

The factoring (number of simplexes n choose k - dependent simplex) x (number of flags on k - independent Euclidean) x (number of flags on n-k - independent Euclidean) = (number of flags on n)

The combinatorial interpretation of n-choose-k counts placements = "external arrangements" n! x...x (n-k+1)! and then divides by the redundancies = "internal arrangements" k! Thus it relates external and internal (within subsystem).

Conjugation gives the ways of relabeling, renaming. For example, (132)(12)(123) relables 1 as 2 and 2 as 3 in (12) to get (23).

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Puslapis paskutinį kartą pakeistas 2018 lapkričio 11 d., 17:25
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