2023
DOI: 10.1017/fms.2023.57
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Remixed Eulerian numbers

Abstract: Remixed Eulerian numbers are a polynomial q-deformation of Postnikov’s mixed Eulerian numbers. They arose naturally in previous work by the authors concerning the permutahedral variety and subsume well-known families of polynomials such as q-binomial coefficients and Garsia–Remmel’s q-hit numbers. We study their combinatorics in more depth. As polynomials in q, they are shown to be symmetric and unimodal. By interpreting them as computing success probabilities in a simple probabilistic process we arrive at a c… Show more

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Cited by 5 publications
(2 citation statements)
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“…For instance, they will help us determine the harmonic polynomials for the ideal QSym + n . The Ω • -correspondence plays a key rule in determining these harmonics and so does the cubical subdivision of the permutahedron discussed in [NT22].…”
Section: Multiplication Of Forest Polynomials Given Nonempty Wordsmentioning
confidence: 99%
See 1 more Smart Citation
“…For instance, they will help us determine the harmonic polynomials for the ideal QSym + n . The Ω • -correspondence plays a key rule in determining these harmonics and so does the cubical subdivision of the permutahedron discussed in [NT22].…”
Section: Multiplication Of Forest Polynomials Given Nonempty Wordsmentioning
confidence: 99%
“…So while we are able to infer positivity of a w via an explicit formula, the expression itself involves summing rational numbers. This aspect motivated a deeper study of mixed Eulerian numbers; see [NT21b,NT22] where a q-analogue is introduced. There has been other recent work utilizing mixed Eulerians in a crucial way; see [BST20,Hor21].…”
mentioning
confidence: 99%