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In Sage, see www.sagemath.org, you find the algorithm G. Brinkmann and B.D. McKay, Fast generation of planar graphs, MATCH-Communications in Mathematical and in Computer Chemistry, 58(2):323-357, 200 …

Okay, I agree that this answer comes actually a little late... If you type some values of your function into FindStat, you will see David Speyer's answer automatically generated, since it is obtained …

I still hope there is a complete (and easy) answer to the question, but as mentioned in my comment above, and since no one else answered so far, I give a description of the inverse map that is not com …

In a joint project, we are currently working on an online combinatorial statistic finder in which (beside other things) want to gather information about combinatorial collections and statistic, see th …

You can search this statistic (normalized so that the smallest value is 0) in www.FindStat.org and you will find that this is the rank of the permutation inside the lattice of alternating sign matrice …

This is far from an answer, but only a possible first part of such a bijection. (There were two plainly wrong bijection parts in the first version that cannot be fixed.) The bijection between factori …

You find Macdonald polynomials defined for root systems for example in Macdonald's lecture series "Symmetric functions and orthogonal polynomaials", or as well in various places, like http://en.wikipe …

Increasing parking functions are in (more or less canonical) bijection with Dyck paths (see, e.g., here), so your question can be rephrased as Is there a direct bijection between (n,n+1)-cores and Dy …

Am I right that you consider $x \mapsto mx$ modulo $mn$? This property is then equivalent to simply consider noncrossing partitions of $\{1,\ldots,mn\}$ where each block has size $n$. Given any multi …

This is Exercise 7.2(f) in Stanley "Enumerative Combinatorics II": The length of the longest chain in dominance order is $$\frac{1}{3}m(m^2+3r-1)$$ where $n = \binom{m+1}{2} + r$ with $0 \leq r \leq m …

This is more a comment, but here I have more space: Did you try to use the characterization of f-vectors of simplicial complexes given by Kruskal in "Joseph B. Kruskal. The number of simplices in a c …

If you have given all linear extensions of $\mathcal{L}(P)$ of a poset $P$. This is the set of all linear orderings (permutations) of the vertex set of $P$ preserving the order in $P$. The order in $P …

Below my modified answer containing a complete bijection between the above sequences and Dyck paths: Let $a = (a_1,\ldots,a_n)$ be a sequence of $n$ integers. $a$ satisfies Property $A$ if it satisfi …

You want to print a deck of cards of the following type: Each card shows $k$ items out of $n$ different items such that any two cards in the deck share exactly one item. Question: What is the bigg …

@PietroMajer's comment essentially contained the answer already: Define a bijection $\phi$ between $k$-multisubsets of $\{ 1,\ldots,n \}$ to $k$-subsets of $\{ 1,\ldots,n+k-1\}$ by sending $\{ c_0 \l …