# Questions tagged [co.combinatorics]

Enumerative combinatorics, graph theory, order theory, posets, matroids, designs and other discrete structures. It also includes algebraic, analytic and probabilistic combinatorics.

6,438 questions
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### What is the six positive real number for a dice producing a highest chance?

Say there is a dice with six faces, each face has a positive real number different from others. There is a chessman on the origin of the number axis. In each trial, the dice rolls infinite times. ...
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### Generalization of Newton's identities to Schur functions

In some recent work, I've stumbled across the following identity for $\lambda \vdash n$: $$n s_\lambda = \sum_{k=1}^n p_k \sum_{\mu \nearrow_k \lambda} (-1)^{\mathrm{ht}(\lambda/\mu)} s_\mu.$$ Here, ...
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### What is the sum of the binomial coefficients ${n\choose p}$ over prime numbers?

What is known about the asymptotics, lower and upper bound of the sum of the binomial coefficients $$S_n = {n\choose 2} + {n\choose 3} + {n\choose 5} + \cdots + {n\choose p}$$ where the sum runs ...