User:Ludovic Schwob

I am a PhD student at LIGM, Université Gustave Eiffel, France. I am interested in combinatorics, arithmetics, geometry...

Contributed sequences

Polygons

Created

A309318: Number of polygons whose vertices are the (2*n+1)-th roots of unity and whose 2*n+1 sides all have distinct slopes.

A330660: Number of polygons formed by connecting the vertices of a regular {2*n+1}-gon such that they make k turns around the center point.

A330662: Number of polygons with 2*n sides, of which k run through the center of a circle, on the circumference of which the 2*n vertices of the polygon are arranged at equal spacing.

A342968: Number of n+2-sided polygons with the property that one makes k turns on itself while following its edges.

A343257: Number of n+2-sided polygons whose points lie on a circle and with the property that one makes k turns on itself, always in the same direction (right or left) while following its edges.

A343369: Number of polygons formed by connecting the vertices of a regular 2n-gon such that the winding number around the center is k and with no side passing through the center.

A358328: Number of polygons with 2*n sides, of which k run through the center of a circle, on the circumference of which the 2*n vertices of the polygon are arranged at equal spacing, up to rotation.

A358329: Number of polygons with 2*n sides, of which k run through the center of a circle, on the circumference of which the 2*n vertices of the polygon are arranged at equal spacing, up to rotation and reflection.

A365094: Number of n-sided cycles with the property that one makes k turns to the right while following its edges.

A371611: Number of 2*n-sided cycles with the property that one makes the same number of left and right turns while following its edges.

A384630: Number of self-inverse double cosets in Z_n\S_n/Z_n (self-inverse cycles).

A384631: Number of self-inverse double cosets in D_n\S_n/D_n (self-inverse polygons).

Computed more terms

A295264: Number of total cyclic orders Z on {0, ..., n-1} such that (i, (i+1) mod n, (i+2) mod n) in Z for 0 <= i < n.

A357602: Number of asymmetric polygons up to symmetry.

Matrices and Young Tableaux

Created

A359856: Number of permutations of [1..n] which are indecomposable by direct and skew sums.

A363689: Number of alternating sign matrices of size n which are indecomposable by direct and skew sums.

A365961: Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums.

A370723: Number of symmetric (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums.

A370396: Number of nonnegative integer matrices with sum of entries equal to 2*n or 2*n+1, no zero rows or columns, which are symmetric about both diagonals.

A373027: Number of (0,1)-matrices with sum of entries equal to 2*n or 2*n+1, no zero rows or columns, which are centrally symmetric.

Computed more terms

A068313: Number of (0,1)-matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums.

A178718: Sum of entries of n-th Kostka matrix for the partitions of n.

A224879: Number of equivalence classes of n X n nonsingular matrices over GF(2), up to row and column permutation.

A299968: Number of normal generalized Young tableaux of size n with all rows and columns strictly increasing.

A321652: Number of nonnegative integer matrices with sum of entries equal to n and no zero rows or columns, with weakly decreasing row sums and column sums.

A321737: Number of ways to partition the Young diagram of an integer partition of n into vertical sections.

A321734: Number of nonnegative integer square matrices with sum of entries equal to n, no zero rows or columns, weakly decreasing row and column sums, and the same row sums as column sums.

A231498: Dimensions of algebraic generators of Hopf algebra ASM.

A231499: Dimensions of totally primitive elements of Hopf algebra ASM.

A374514: Number of n X n matrices whose values cover an initial interval of positive integers and whose rows and columns have values which are strictly increasing.

In the following table, $\lambda ⊢n$ is an integer partition of $n$, $K_{\lambda ,\mu }$ are Kostka numbers and $a_{\lambda }=\frac{(\sum _i{m}_i)!}{\prod _i{m}_i!}$ where $m_i$ are the multiplicities of $\lambda$.

	Number of $\{0,1\}$-Matrices with no zero row and column and sum $n$.	Number of $\mathbf{𝐍}$-Matrices with no zero row and column and sum $n$.
All	1, 4, 24, 196, 2016, 24976, 361792... (A101370) $a(n)=\sum _{\lambda ,\mu ,\nu ⊢n}{a}_{\mu }{a}_{\nu }{K}_{\lambda \mu }{K}_{\bar{\lambda }\nu }$	1, 5, 33, 281, 2961, 37277, 546193... (A120733) $a(n)=\sum _{\lambda ,\mu ,\nu ⊢n}{a}_{\mu }{a}_{\nu }{K}_{\lambda \mu }{K}_{\lambda \nu }$
Up to permutation of rows	1, 3, 10, 41, 192, 1025, 6087, 39754... (A116540)
Up to permutation of rows and columns	1, 3, 6, 16, 34, 90, 211, 558, 1430, 3908... (A049311)	1, 4, 10, 33, 91, 298, 910, 3017, 9945... (A007716)
Symmetric	1, 2, 6, 20, 74, 302, 1314, 6122, 29982... (A135588)	1, 3, 9, 33, 125, 531, 2349, 11205, 55589... (A138178) $a(n)=\sum _{\lambda ,\mu ⊢n}{a}_{\mu }{K}_{\lambda \mu }$
Square	1, 2, 10, 70, 642, 7246, 97052, 1503700... (A104602) $a(n)=\sum _{\underset{l(\mu )=l(\nu )}{\lambda ,\mu ,\nu ⊢n}}{a}_{\mu }{a}_{\nu }{K}_{\lambda \mu }{K}_{\bar{\lambda }\nu }$	1, 3, 15, 107, 991, 11267, 151721... (A120732) $a(n)=\sum _{\underset{l(\mu )=l(\nu )}{\lambda ,\mu ,\nu ⊢n}}{a}_{\mu }{a}_{\nu }{K}_{\lambda \mu }{K}_{\lambda \nu }$
Equal row and column sums	1, 2, 8, 40, 246, 1816, 15630, 153592... (A321733) $a(n)=\sum _{\lambda ,\mu ⊢n}{a}_{\mu }{K}_{\lambda \mu }{K}_{\bar{\lambda }\mu }$	1, 3, 11, 53, 317, 2293, 19435, 188851... (A321732) $a(n)=\sum _{\lambda ,\mu ⊢n}{a}_{\mu }{K}_{\lambda \mu }^2$
Nonincreasing row sums	1, 4, 19, 127, 967, 9063, 94595, 1139708... (A365961) $a(n)=\sum _{\lambda ,\mu ,\nu ⊢n}{a}_{\mu }{K}_{\lambda \mu }{K}_{\bar{\lambda }\nu }$	1, 5, 25, 173, 1297, 12225, 124997... (A035341) $a(n)=\sum _{\lambda ,\mu ,\nu ⊢n}{a}_{\mu }{K}_{\lambda \mu }{K}_{\lambda \nu }$
Nonincreasing row and column sums	1, 4, 15, 82, 457, 3231, 24055, 209375... (A068313) $a(n)=\sum _{\lambda ,\mu ,\nu ⊢n}{K}_{\lambda \mu }{K}_{\bar{\lambda }\nu }$	1, 5, 19, 107, 573, 4050, 29093, 249301... (A321652) $a(n)=\sum _{\lambda ,\mu ,\nu ⊢n}{K}_{\lambda \mu }{K}_{\lambda \nu }$
Nonincreasing and equal row and column sums	1, 2, 7, 30, 153, 939, 6653, 53743... (A321735) $a(n)=\sum _{\lambda ,\mu ⊢n}{K}_{\lambda \mu }{K}_{\bar{\lambda }\mu }$	1, 3, 9, 37, 177, 1054, 7237, 57447... (A321734) $a(n)=\sum _{\lambda ,\mu ⊢n}{K}_{\lambda \mu }^2$
Symmetric, nonincreasing row and column sums	1, 2, 5, 14, 39, 123, 393... (A370723)	1, 3, 7, 21, 57, 182, 565, 1931, 6670... (A178718) $a(n)=\sum _{\lambda ,\mu ⊢n}{K}_{\lambda \mu }$

Lattices

Created

A374153: Number of domino tilings of the order n Aztec diamond which are diagonally symmetric.

A374154: Number of domino tilings of the order n Aztec diamond which are diagonally and antidiagonally symmetric.

A377408: Number of unlabeled semidistributive lattices with n elements.

A378072: Number of elements in the completion of the Bruhat order on B_n.

A378173: Number of proper antichain partitions of the rectangular poset of size n X k.

A379034: Number of intervals in the lattice of Motzkin paths of length n.

A379035: Number of intervals in the lattice of Schroeder paths of length 2*n.

A382507: Number of half turn symmetric lattice congruences of the weak order on the symmetric group S_n.

A382829: Number of distinct rank vectors of distributive lattices of height n.

A383372: Number of centrally symmetric Baxter permutations of length n.

A384133: Number of linear intervals of height k in the Tamari lattice Tam_n.

A391308: Number of linear intervals of height k in the weak order on permutations of length n.

A387943: Number of fully packed loops on an n X n grid with no cycle.

A389288: Number of nested pairs of Dyck paths of lengths n and n+1.

A389236: Number of alternating sign hypermatrix Latin-like squares of size n.

A390149: Number of rhombus tilings of a triangular shape formed by n*(n+1)/2 adjacent hexagons.

A390341: Number of vertically centered alternating sign matrices of size 2*n+1.

A391690: Number of congruences of the lattice of alternating sign matrices of size n such that minima of congruence classes are permutations.

A391691: Number of congruences of the lattice of alternating sign matrices of size n such that minima and maxima of congruence classes are permutations.

A391692: Number of distinct sets of the form J(P_s)\J(P_t) where s > t are two permutations of size n differing by a transposition and J(M) is the set of join-irreducible elements below M in the lattice of alternating sign matrices.

A391955: Number of pairs of Dyck paths of length 2*n touching the axis at the same points.

A391969: Number of quotients of the lattice of alternating sign matrices of size n isomorphic to the lattice of Dyck paths of length 2*n.

A390493: Number of symmetric catalan triangles of size n.

A391973: Number of self-dual catalan triangles of size 2*n+1.

Computed more terms

A180349: Number of gapless triangles of size n.

Others

Created

A347521: Number of polyominoes with n cells formed by coordinates that are not coprime.

A366020: Number of polyominoes in which every cell has coprime coordinates.

A327662: Length of shortest word of frequency depth n.

A340002: Random walk in R^3: Numerators of the expected distance after n steps.

A340003: Random walk in R^3: Denominators of the expected distance after n steps.

A346797: Number of partitions of n into parts congruent to 0, 2 or 5 (mod 7).

A346798: Number of partitions of n into parts congruent to 0, 3 or 4 (mod 7).

A360154: Primes of the form m^2 + 2*k^2 such that m^2 + 2*(k+1)^2 is also prime.

A360155: Primes of the form m^2 + 2*(k+1)^2 such that m^2 + 2*k^2 is also prime.

A360985: Number of full binary trees with n leaves, each internal node having the heights of its two subtrees weakly increasing left to right, and with k internal nodes having two subtrees of equal height.

A363685: Number of descending plane partitions of order n with the sum of the parts equal to k.

A382440: Number of rooted full binary trees with n internal nodes, up to their multiset of subtree sizes.

A383894: Number of arborescent partitions with exactly n parts.

A383895: Number of spiny partitions with exactly n parts.

A383370: Number of partial orders on {1,2,...,n} that are contained in the usual linear order, whose dual is given by the relabelling k -> n+1-k.

Computed more terms

A308399: Number of partitions of n into parts congruent to 0, 3, or 5 (mod 8).

A082733: Sum of all entries in character table of the symmetric group S_n.

A094907: Number of different nontrivial two-digit cancellations of the form (xy)/(zx) = y/z in base n.

A247139: Number of tilings of a triangular shape T_n with n rectangles identifying all tilings which use the same rectangular shapes.

A256330: Number of H&S Family matchings on n edges.

A300697 and A300698: Volumes of concertina hypercubes.

A317553: Sum of coefficients in the expansion of Sum_{y a composition of n} p(y) in terms of Schur functions, where p is power-sum symmetric functions.