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I would like to know if there are existing results on the following objects: spanning trees of a grid graph, with no corridor where a corridor is a vertex having exactly two neighbors, on opposi …

This property ( or rather the generalized version by Darij using (a,b)-shuffles ) means that f is what is called a "symmetral mould" in the context of Ecalle's theory of moulds. There is a related not …

Fricas is good at that. It can be accessed via sage, once installed. sage: L=[catalan_number(i) for i in range(20)] sage: fricas.guessHolo(L) …

this could be done in sage: sage: B3 = WeylCharacterRing("B3", style="coroots") sage: spin = B3(0,0,1) sage: spin.symmetric_power(6) B3(0,0,0) + B3(0,0,2) + B3(0,0,4) + B3(0,0,6) sage: A3 = WeylChar …

Let $n \geq 1$ be an integer and consider the symmetric function $$D_n = \sum_{d|n} p_d^{n/d},$$ where $p_{d}$ are the power-sum symmetric functions. It can be checked up to $n=35$ that the symmetric …

Let $P_i$ be the power sum symmetric function. In your $p_n$, Replace $x+\gamma$ by $P_1$ and $\zeta(i)$ by $P_i$. Then divide the result by $n!$. What you get looks like a well-known symmetric functi …

This is a question about universality in probability theory, with combinatorics in mind. Consider a sequence of polynomials $P_n$ in one variable, with positive coefficients. Combinatorics is a large …

This has been considered by Dimitri Zvonkine, see his article "An algebra of power series arising in the intersection theory of moduli spaces of curves and in the enumeration of ramified coverings of …

There are some ad-hoc definitions for some types. Type B can be defined using diagrams that have a left-right symmetry. Tammo tom Dieck has proposed a definition for type D here: (http://www.uni-math. …

Sagemath can do that too sage: x = PowerSeriesRing(QQ,'x').gen() sage: f = sum(x**n/(n+1)**2 for n in range(20)).O(20) sage: f.jacobi_continued_fraction() ((-1/4, -7/144), (-13/28, -647/110 …

When rephrased (using the positive generating series $g=-f$) as the identity $g(-g(-t))=t$, this suggests that there may exist a quadratic nonsymmetric operad with this generating series, which is Kos …

Let $P$ be a finite poset (partially ordered set). I am wondering whether the following condition on $P$ has been studied somewhere: (#) No interval $[a,b]$ in $P$ has $3$ elements. Note that interv …

Regarding question Q2, one can go a little bit further and describe simple diagrams with few edges for some more cases. Let us talk about $Gr(p, p+q)$, so that there is a symmetry between $p$ and $q$. …

This set of lattices is the closure of the set {poset with one element} under two allowed operations: adding a top element or taking a Cartesian product. This implies that the Möbius numbers are in $\ …

There is not much known in general, as far as I know. There is a nice 2-form (called the Weil-Petersson 2-form) defined using the cluster algebra structure. This can be found in article "The Weil-Pe …