An explicit arrangement of n hyperplanes in 3-space indexes binary 2-binomial equivalence classes of binary words of length n, with class sizes given by coefficients of Gaussian binomials.
Richomme, On some 2 -binomial coefficients of binary words: geometrical interpretation, partitions of integers, and fair words, Theoret.\ Comput.\ Sci.\ 1066 (2026), Paper No
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Binary binomial equivalence via hyperplane arrangements
An explicit arrangement of n hyperplanes in 3-space indexes binary 2-binomial equivalence classes of binary words of length n, with class sizes given by coefficients of Gaussian binomials.