Jiang Zeng

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20182026

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math.CO2026

A Fixed-Point Worpitzky Identity and a Positive Binomial Transform for Type $B$ Involutions

Jiang Zeng

Let $I_{n}^{B}$ be the involutions of the hyperoctahedral group $B_{n}$ , and let $\des^B$ denote the descent number with respect to the natural Coxeter order. We deriv…

math.CO2026

Higher-Order Cyclotomic Congruences for $q$ -Secant and Generalized $q$ -Euler Numbers

Jiang Zeng

Let $\A(2n)$ denote the set of up--down alternating permutations of ${1, 2, \dots, 2 n}$ , and let \[ E_{2n}(q)=\sum_{σ\in\A(2n)}q^{\operatorname{inv}(σ)}. \] Andrews and Foata prove…

A Fixed-Point Worpitzky Identity and a Positive Binomial Transform for Type B Involutions

Higher-Order Cyclotomic Congruences for q-Secant and Generalized q-Euler Numbers

A Fixed-Point Worpitzky Identity and a Positive Binomial Transform for Type $B$ Involutions

Higher-Order Cyclotomic Congruences for $q$ -Secant and Generalized $q$ -Euler Numbers