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Richard Stanley suggested the problem of finding combinatorial proofs of formulas for counting regions of certain hyperplane arrangements defined by hyperplanes of the form $x_i=0$, $x_i=x_j$, and $x_i=2x_j$ that were found using the finite field method. We give such proofs, using embroidered permutations and linear extensions of posets.
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참고문헌 (12)
참고문헌 신청
F. Ardila / 2007 / Computing the Tutte polynomial of a hyperplane arrangement / Pacific J. Math 230(1):1~26
C. A. Athanasiadis / 1996 / Characteristic polynomials of subspace arrangements and finite fields / Adv. Math 122(2):193~233
H. H. Crapo / 1970 / On the foundations of combinatorial theory: Combinatorial geometries / The M.I.T. Press
S.-P. Eu / 2005 / On the enumeration of parking functions by leading terms / Adv. in Appl. Math 35(4):392~406
J. P. S. Kung / 2003 / Goncarov polynomials and parking functions / J. Combin. Theory Ser. A 102(1):16~37
C. A. Athanasiadis / 1996 / Characteristic polynomials of subspace arrangements and finite fields / Adv. Math 122(2):193~233
H. H. Crapo / 1970 / On the foundations of combinatorial theory: Combinatorial geometries / The M.I.T. Press
S.-P. Eu / 2005 / On the enumeration of parking functions by leading terms / Adv. in Appl. Math 35(4):392~406
J. P. S. Kung / 2003 / Goncarov polynomials and parking functions / J. Combin. Theory Ser. A 102(1):16~37
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