\(q\)-analogs of the inclusion-exclusion principle and permutations with restricted position

DOI10.1016/0012-365X(92)90622-MzbMath0806.05010MaRDI QIDQ1197002

William Y. C. Chen, Gian-Carlo Rota

Publication date: 16 January 1993

Published in: Discrete Mathematics (Search for Journal in Brave)

zbMATH Keywords

Mahonian statisticsKaplansky-Riordan theorypermutations with restricted positionprinciple of inclusion-exclusion

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Combinatorial identities, bijective combinatorics (05A19) (q)-calculus and related topics (05A30) Permutations, words, matrices (05A05) Vector spaces, linear dependence, rank, lineability (15A03)

Related Items (20)

The \(q\)-log-concavity and unimodality of \(q\)-Kaplansky numbers ⋮ The log-concavity of the \(q\)-derangement numbers of type \(B\) ⋮ Geometric representations of \(\text{GL}(n,R)\), cellular Hecke algebras and the embedding problem. ⋮ On the spiral property of the \(q\)-derangement numbers ⋮ A \(q\)-analog of approximation inclusion-exclusion ⋮ A representation theorem for (\(q\)-)holonomic sequences ⋮ Suboptimal \(s\)-union families and \(s\)-union antichains for vector spaces ⋮ On a kind of sequence of polynomials ⋮ The ratio monotonicity of the \(q\)-derangement numbers ⋮ On derangement polynomials of type \(D\) ⋮ Unnamed Item ⋮ Quotient sets and subset-subspace analogy ⋮ \(q\)-weighted log-concavity and \(q\)-product theorem on the normality of posets ⋮ Unnamed Item ⋮ \(q\)-rook polynomials and matrices over finite fields ⋮ The combinatorics behind number-theoretic sieves ⋮ A combinatorial interpretation of the Seidel generation of \(q\)-derangement numbers ⋮ Kinematic formulas for finite lattices ⋮ Counting permutations with given cycle structure and descent set ⋮ On Some Geometric Representations ofGL_N(𝔬)

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