Results 1 to 10 of about 2,605 (59)
A note on super Catalan numbers [PDF]
, 2012 We show that the super Catalan numbers are special values of the Krawtchouk polynomials by deriving an expression for the super Catalan numbers in terms of a signed set.Comment: 4 pages. Revised and Accepted.
Georgiadis, Evangelos +2 more
core +3 more sources
Hook formulas for skew shapes I. $q$-analogues and bijections [PDF]
, 2018 The celebrated hook-length formula gives a product formula for the number of standard Young tableaux of a straight shape. In 2014, Naruse announced a more general formula for the number of standard Young tableaux of skew shapes as a positive sum over ...
Morales, Alejandro +2 more
core +1 more source
Combinatorially interpreting generalized Stirling numbers [PDF]
, 2014 Let $w$ be a word in alphabet $\{x,D\}$ with $m$ $x$'s and $n$ $D$'s. Interpreting "$x$" as multiplication by $x$, and "$D$" as differentiation with respect to $x$, the identity $wf(x) = x^{m-n}\sum_k S_w(k) x^k D^k f(x)$, valid for any smooth function ...
Engbers, John +2 more
core +4 more sources
A polyhedral model of partitions with bounded differences and a bijective proof of a theorem of Andrews, Beck, and Robbins [PDF]
, 2015 The main result of this paper is a bijective proof showing that the generating function for partitions with bounded differences between largest and smallest part is a rational function.
Breuer, Felix, Kronholm, Brandt
core +3 more sources
A Markov growth process for Macdonald's distribution on reduced words [PDF]
, 2014 We give an algorithmic-bijective proof of Macdonald's reduced word identity in the theory of Schubert polynomials, in the special case where the permutation is dominant.
Young, Benjamin
core
Eulerian idempotent, pre-Lie logarithm and combinatorics of trees [PDF]
, 2017 The aim of this paper is to bring together the three objects in the title. Recall that, given a Lie algebra $\mathfrak{g}$, the Eulerian idempotent is a canonical projection from the enveloping algebra $U(\mathfrak{g})$ to $\mathfrak{g}$.
Bandiera, Ruggero, Schaetz, Florian
core +1 more source
Skew Schubert functions and the Pieri formula for flag manifolds
, 1997 We show the equivalence of the Pieri formula for flag manifolds and certain identities among the structure constants, giving new proofs of both the Pieri formula and of these identities.
Bergeron, Nantel, Sottile, Frank
core +3 more sources
Decomposition spaces in combinatorics [PDF]
, 2016 A decomposition space (also called unital 2-Segal space) is a simplicial object satisfying an exactness condition weaker than the Segal condition: just as the Segal condition expresses (up to homotopy) composition, the new condition expresses ...
Gálvez Carrillo, Maria Immaculada +2 more
core +1 more source
Combinatorics of poly-Bernoulli numbers
, 2015 The ${\mathbb B}_n^{(k)}$ poly-Bernoulli numbers --- a natural generalization of classical Bernoulli numbers ($B_n={\mathbb B}_n^{(1)}$) --- were introduced by Kaneko in 1997. When the parameter $k$ is negative then ${\mathbb B}_n^{(k)}$ is a nonnegative
Bényi, Beáta, Hajnal, Peter
core +1 more source
Polynomial Triangles Revisited [PDF]
, 2012 A polynomial triangle is an array whose inputs are the coefficients in integral powers of a polynomial. Although polynomial coefficients have appeared in several works, there is no systematic treatise on this topic. In this paper we plan to fill this gap.
Mohammedia Morocco, Nour-eddine Fahssi
core